

Hi
Wonder if anyone could point me how I use this method to discover
the half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to discretise the equation and then fit the data to it. I don't have the time right now to go into all the details but it's not hard you can parameterise the process using simple linear regression. If you need help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the half life of a mean reverting process.
I am looking into pair trading and the time it takes for a cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


In reply to this post by Stephen Choularton3
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_modelfor the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn
> 
>
> Message: 2
> Date: Tue, 12 Oct 2010 05:43:32 0400
> From: Sarbo < [hidden email]>
> To: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> MessageID: < [hidden email]>
> ContentType: text/plain; charset="utf8"
>
> By halflife, do you mean the speed of meanreversion?
>
> If so, there's a bit of algebraic tomfoolery that's required to
> discretise the equation and then fit the data to it. I don't have the
> time right now to go into all the details but it's not hard you can
> parameterise the process using simple linear regression. If you need
> help with that I'll try and get back to you tonight about it.
>
> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>
> > Hi
> >
> > Wonder if anyone could point me how I use this method to discover the
> > half life of a mean reverting process.
> >
> > I am looking into pair trading and the time it takes for a
> > cointegrated pair to revert to the norm.
> >
> > 
> > Stephen Choularton Ph.D., FIoD
> >
> > 9999 2226
> > 0413 545 182
> >
> >
> > for insurance go to www.netinsure.com.au
> > for markets go to www.organicfoodmarkets.com.au
> >
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R questions
> should go.
>
>
>  next part 
> An HTML attachment was scrubbed...
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html> >
>  next part 
> A nontext attachment was scrubbed...
> Name: CoS2010Winner.JPG
> Type: image/jpeg
> Size: 16091 bytes
> Desc: not available
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe> >
>
> 
>
> _______________________________________________
> RSIGFinance mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>
>
> End of RSIGFinance Digest, Vol 77, Issue 8
> ********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Stephen:
I do meanreversion trading, and I use a halflife analysis to judge the
wisdom of a trade. If the estimated halflife is too long, it doesn't make
sense to take the trade. It's a timevsrisk thing.
In the past, I used the log(2)/speed formula mentioned by Bjorn, below. (His
link is very useful, BTW.) However, I was very unhappy with the estimates
provided by that formula. They did not match my actual trading experience.
I did some research on the topic, and got some useful results. I added a
momentum term to my model, measuruing the current slope of the spread. The
slope answers an important question: is the spread currently reverting
(moving towards the mean) or is it averting (moving away from the mean)? The
halflife is different, depending upon the current phase (reversion vs.
aversion). I found this conditioning term was statistically significant, so
I condition my estimate on it. I generate historical data and partition it
according to the market's reversion/aversion state. The two partitions shows
a different halflife, with the reverting phase having a (much) shorter
halflife than the averting phase. Both phases show an exponentally
distributed halflife, but with different means. I use those historical
estimates now in my trading, instead of the OU estimate.
In retrospect, the problem with the OU model is that it assumes the
meanreverting process is always reverting. That is not quite correct. In my
experience, the spreads can alternate between periods of meanaversion and
meanreversion.
I hope that helps (and I hope it makes sense!).
Paul
Original Message
From: [hidden email]
[mailto: [hidden email]] On Behalf Of Bjorn Skogtro
Sent: Tuesday, October 12, 2010 5:34 AM
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_modelfor the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjxrn
> 
>
> Message: 2
> Date: Tue, 12 Oct 2010 05:43:32 0400
> From: Sarbo < [hidden email]>
> To: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> MessageID: < [hidden email]>
> ContentType: text/plain; charset="utf8"
>
> By halflife, do you mean the speed of meanreversion?
>
> If so, there's a bit of algebraic tomfoolery that's required to
> discretise the equation and then fit the data to it. I don't have the
> time right now to go into all the details but it's not hard you can
> parameterise the process using simple linear regression. If you need
> help with that I'll try and get back to you tonight about it.
>
> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>
> > Hi
> >
> > Wonder if anyone could point me how I use this method to discover
> > the half life of a mean reverting process.
> >
> > I am looking into pair trading and the time it takes for a
> > cointegrated pair to revert to the norm.
> >
> > 
> > Stephen Choularton Ph.D., FIoD
> >
> > 9999 2226
> > 0413 545 182
> >
> >
> > for insurance go to www.netinsure.com.au for markets go to
> > www.organicfoodmarkets.com.au
> >
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R
> > questions
> should go.
>
>
>  next part  An HTML attachment was
> scrubbed...
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e3> 2fc7/attachment0001.html
> >
>  next part  A nontext attachment was
> scrubbed...
> Name: CoS2010Winner.JPG
> Type: image/jpeg
> Size: 16091 bytes
> Desc: not available
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e3> 2fc7/attachment0001.jpe
> >
>
> 
>
> _______________________________________________
> RSIGFinance mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>
>
> End of RSIGFinance Digest, Vol 77, Issue 8
> ********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
> Hi Stephen,
>
> You could take a look at
>
> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>
> for the linear regression method, or take a look at the package "sde" which
> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
> though, only the CIR).
>
> The halflife is given as log(2)/meanreversion speed.
>
> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
> are using (daily, yearly) for interpreting the halflife.
>
> BR,
> Bjørn
>
>
>
>
>
>
>> 
>>
>> Message: 2
>> Date: Tue, 12 Oct 2010 05:43:32 0400
>> From: Sarbo < [hidden email]>
>> To: [hidden email]
>> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>> MessageID: < [hidden email]>
>> ContentType: text/plain; charset="utf8"
>>
>> By halflife, do you mean the speed of meanreversion?
>>
>> If so, there's a bit of algebraic tomfoolery that's required to
>> discretise the equation and then fit the data to it. I don't have the
>> time right now to go into all the details but it's not hard you can
>> parameterise the process using simple linear regression. If you need
>> help with that I'll try and get back to you tonight about it.
>>
>> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>>
>>> Hi
>>>
>>> Wonder if anyone could point me how I use this method to discover the
>>> half life of a mean reverting process.
>>>
>>> I am looking into pair trading and the time it takes for a
>>> cointegrated pair to revert to the norm.
>>>
>>> 
>>> Stephen Choularton Ph.D., FIoD
>>>
>>> 9999 2226
>>> 0413 545 182
>>>
>>>
>>> for insurance go to www.netinsure.com.au
>>> for markets go to www.organicfoodmarkets.com.au
>>>
>>>
>>> _______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>  Subscriberposting only. If you want to post, subscribe first.
>>>  Also note that this is not the rhelp list where general R questions
>> should go.
>>
>>
>>  next part 
>> An HTML attachment was scrubbed...
>> URL: <
>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>>>
>>  next part 
>> A nontext attachment was scrubbed...
>> Name: CoS2010Winner.JPG
>> Type: image/jpeg
>> Size: 16091 bytes
>> Desc: not available
>> URL: <
>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>>>
>>
>> 
>>
>> _______________________________________________
>> RSIGFinance mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>
>>
>> End of RSIGFinance Digest, Vol 77, Issue 8
>> ********************************************
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus
Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Just another thought:
If you google around, you may stumble upon some results on first passage
times for the OUprocess that may be useful to you. These are known in an
closedform solution.
I think, like Paul, that polishing the strategy is essential. Finding
reverting pairs are the easy part, but optimizing the entry/exit signals are
the trick.
Bjørn
PS: A simple code for calibrating the OUprocess. Should've attached this
the first time :)
#source("ouFit.R")
ouFit=function(spread) {
n=length(spread)
x=spread[1:(n1)]
y=spread[2:n]
spread.fit=lm(y~x)
coefs=as.numeric(coefficients(spread.fit))
a=coefs[1]
b=coefs[2]
err=var(residuals(spread.fit))
alpha=log(a)
mu=alpha*b/(1a)
sigma=sqrt(2*alpha*err/(1a^2))
theta=list(alpha=alpha, mu=mu, sigma=sigma)
return(theta)
}
It won't give you halflife, but you can use the alpha from the above code
to find it, in combination with my previous post.
2010/10/12 Paul Teetor < [hidden email]>
> Stephen:
>
> I do meanreversion trading, and I use a halflife analysis to judge the
> wisdom of a trade. If the estimated halflife is too long, it doesn't make
> sense to take the trade. It's a timevsrisk thing.
>
> In the past, I used the log(2)/speed formula mentioned by Bjorn, below.
> (His
> link is very useful, BTW.) However, I was very unhappy with the estimates
> provided by that formula. They did not match my actual trading experience.
>
> I did some research on the topic, and got some useful results. I added a
> momentum term to my model, measuruing the current slope of the spread. The
> slope answers an important question: is the spread currently reverting
> (moving towards the mean) or is it averting (moving away from the mean)?
> The
> halflife is different, depending upon the current phase (reversion vs.
> aversion). I found this conditioning term was statistically significant, so
> I condition my estimate on it. I generate historical data and partition it
> according to the market's reversion/aversion state. The two partitions
> shows
> a different halflife, with the reverting phase having a (much) shorter
> halflife than the averting phase. Both phases show an exponentally
> distributed halflife, but with different means. I use those historical
> estimates now in my trading, instead of the OU estimate.
>
> In retrospect, the problem with the OU model is that it assumes the
> meanreverting process is always reverting. That is not quite correct. In
> my
> experience, the spreads can alternate between periods of meanaversion and
> meanreversion.
>
> I hope that helps (and I hope it makes sense!).
>
> Paul
>
>
> Original Message
> From: [hidden email]
> [mailto: [hidden email]] On Behalf Of Bjorn
> Skogtro
> Sent: Tuesday, October 12, 2010 5:34 AM
> To: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>
> Hi Stephen,
>
> You could take a look at
>
> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>
> for the linear regression method, or take a look at the package "sde" which
> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
> though, only the CIR).
>
> The halflife is given as log(2)/meanreversion speed.
>
> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
> are using (daily, yearly) for interpreting the halflife.
>
> BR,
> Bjxrn
>
>
>
>
>
>
> > 
> >
> > Message: 2
> > Date: Tue, 12 Oct 2010 05:43:32 0400
> > From: Sarbo < [hidden email]>
> > To: [hidden email]
> > Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> > MessageID: < [hidden email]>
> > ContentType: text/plain; charset="utf8"
> >
> > By halflife, do you mean the speed of meanreversion?
> >
> > If so, there's a bit of algebraic tomfoolery that's required to
> > discretise the equation and then fit the data to it. I don't have the
> > time right now to go into all the details but it's not hard you can
> > parameterise the process using simple linear regression. If you need
> > help with that I'll try and get back to you tonight about it.
> >
> > On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
> >
> > > Hi
> > >
> > > Wonder if anyone could point me how I use this method to discover
> > > the half life of a mean reverting process.
> > >
> > > I am looking into pair trading and the time it takes for a
> > > cointegrated pair to revert to the norm.
> > >
> > > 
> > > Stephen Choularton Ph.D., FIoD
> > >
> > > 9999 2226
> > > 0413 545 182
> > >
> > >
> > > for insurance go to www.netinsure.com.au for markets go to
> > > www.organicfoodmarkets.com.au
> > >
> > >
> > > _______________________________________________
> > > [hidden email] mailing list
> > > https://stat.ethz.ch/mailman/listinfo/rsigfinance> > >  Subscriberposting only. If you want to post, subscribe first.
> > >  Also note that this is not the rhelp list where general R
> > > questions
> > should go.
> >
> >
> >  next part  An HTML attachment was
> > scrubbed...
> > URL: <
> > https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e3> > 2fc7/attachment0001.html
> > >
> >  next part  A nontext attachment was
> > scrubbed...
> > Name: CoS2010Winner.JPG
> > Type: image/jpeg
> > Size: 16091 bytes
> > Desc: not available
> > URL: <
> > https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e3> > 2fc7/attachment0001.jpe
> > >
> >
> > 
> >
> > _______________________________________________
> > RSIGFinance mailing list
> > [hidden email]
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >
> >
> > End of RSIGFinance Digest, Vol 77, Issue 8
> > ********************************************
>
> [[alternative HTML version deleted]]
>
>
>

Up, down, turn around
Please dont let me hit the ground
Tonight I think Ill walk alone
Ill find my soul as I go home.
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


The OU process is Gaussian, but the
market didn't get the memo that *it*
has to be Gaussian.
On 12/10/2010 16:41, stefano iacus wrote:
> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>
> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>
> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>
>
> # ex3.01.R
> OU.lik< function(theta1, theta2, theta3){
> n< length(X)
> dt< deltat(X)
> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> }
>
> require(stats4)
> require(sde)
> set.seed(123)
> X< sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit
> summary(fit)
>
> # ex3.01.R (cont.)
> prof< profile(fit)
> par(mfrow=c(1,3))
> plot(prof)
> par(mfrow=c(1,1))
> vcov(fit)
> confint(fit)
>
> # ex3.01.R (cont.)
> set.seed(123)
> X< sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit2
> summary(fit2)
>
>
> I hope this helps out
>
> stefano
>
> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>
>> Hi Stephen,
>>
>> You could take a look at
>>
>> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>>
>> for the linear regression method, or take a look at the package "sde" which
>> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
>> though, only the CIR).
>>
>> The halflife is given as log(2)/meanreversion speed.
>>
>> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
>> are using (daily, yearly) for interpreting the halflife.
>>
>> BR,
>> Bjørn
>>
>>
>>
>>
>>
>>
>>> 
>>>
>>> Message: 2
>>> Date: Tue, 12 Oct 2010 05:43:32 0400
>>> From: Sarbo< [hidden email]>
>>> To: [hidden email]
>>> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>>> MessageID:< [hidden email]>
>>> ContentType: text/plain; charset="utf8"
>>>
>>> By halflife, do you mean the speed of meanreversion?
>>>
>>> If so, there's a bit of algebraic tomfoolery that's required to
>>> discretise the equation and then fit the data to it. I don't have the
>>> time right now to go into all the details but it's not hard you can
>>> parameterise the process using simple linear regression. If you need
>>> help with that I'll try and get back to you tonight about it.
>>>
>>> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>>>
>>>> Hi
>>>>
>>>> Wonder if anyone could point me how I use this method to discover the
>>>> half life of a mean reverting process.
>>>>
>>>> I am looking into pair trading and the time it takes for a
>>>> cointegrated pair to revert to the norm.
>>>>
>>>> 
>>>> Stephen Choularton Ph.D., FIoD
>>>>
>>>> 9999 2226
>>>> 0413 545 182
>>>>
>>>>
>>>> for insurance go to www.netinsure.com.au
>>>> for markets go to www.organicfoodmarkets.com.au
>>>>
>>>>
>>>> _______________________________________________
>>>> [hidden email] mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>>  Subscriberposting only. If you want to post, subscribe first.
>>>>  Also note that this is not the rhelp list where general R questions
>>> should go.
>>>
>>>
>>>  next part 
>>> An HTML attachment was scrubbed...
>>> URL:<
>>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>>>>
>>>  next part 
>>> A nontext attachment was scrubbed...
>>> Name: CoS2010Winner.JPG
>>> Type: image/jpeg
>>> Size: 16091 bytes
>>> Desc: not available
>>> URL:<
>>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>>>>
>>>
>>> 
>>>
>>> _______________________________________________
>>> RSIGFinance mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>
>>>
>>> End of RSIGFinance Digest, Vol 77, Issue 8
>>> ********************************************
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions should go.
>
>
> 
> Stefano M. Iacus
> Department of Economics,
> Business and Statistics
> University of Milan
> Via Conservatorio, 7
> I20123 Milan  Italy
> Ph.: +39 02 50321 461
> Fax: +39 02 50321 505
> http://www.economia.unimi.it/iacus> 
> Please don't send me Word or PowerPoint attachments if not
> absolutely necessary. See:
> http://www.gnu.org/philosophy/nowordattachments.html>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>

Patrick Burns
[hidden email]
http://www.burnsstat.comhttp://www.portfolioprobe.com/blog_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


that's another point and I completely agree with you :)
so the real point is not trying to fit wrong models on the (so to say) "wrong" data
stefano
On 12 Oct 2010, at 18:00, Patrick Burns wrote:
> The OU process is Gaussian, but the
> market didn't get the memo that *it*
> has to be Gaussian.
>
> On 12/10/2010 16:41, stefano iacus wrote:
>> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>>
>> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>>
>> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>>
>>
>> # ex3.01.R
>> OU.lik< function(theta1, theta2, theta3){
>> n< length(X)
>> dt< deltat(X)
>> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
>> }
>>
>> require(stats4)
>> require(sde)
>> set.seed(123)
>> X< sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit
>> summary(fit)
>>
>> # ex3.01.R (cont.)
>> prof< profile(fit)
>> par(mfrow=c(1,3))
>> plot(prof)
>> par(mfrow=c(1,1))
>> vcov(fit)
>> confint(fit)
>>
>> # ex3.01.R (cont.)
>> set.seed(123)
>> X< sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit2
>> summary(fit2)
>>
>>
>> I hope this helps out
>>
>> stefano
>>
>> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>>
>>> Hi Stephen,
>>>
>>> You could take a look at
>>>
>>> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>>>
>>> for the linear regression method, or take a look at the package "sde" which
>>> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
>>> though, only the CIR).
>>>
>>> The halflife is given as log(2)/meanreversion speed.
>>>
>>> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
>>> are using (daily, yearly) for interpreting the halflife.
>>>
>>> BR,
>>> Bjørn
>>>
>>>
>>>
>>>
>>>
>>>
>>>> 
>>>>
>>>> Message: 2
>>>> Date: Tue, 12 Oct 2010 05:43:32 0400
>>>> From: Sarbo< [hidden email]>
>>>> To: [hidden email]
>>>> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>>>> MessageID:< [hidden email]>
>>>> ContentType: text/plain; charset="utf8"
>>>>
>>>> By halflife, do you mean the speed of meanreversion?
>>>>
>>>> If so, there's a bit of algebraic tomfoolery that's required to
>>>> discretise the equation and then fit the data to it. I don't have the
>>>> time right now to go into all the details but it's not hard you can
>>>> parameterise the process using simple linear regression. If you need
>>>> help with that I'll try and get back to you tonight about it.
>>>>
>>>> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>>>>
>>>>> Hi
>>>>>
>>>>> Wonder if anyone could point me how I use this method to discover the
>>>>> half life of a mean reverting process.
>>>>>
>>>>> I am looking into pair trading and the time it takes for a
>>>>> cointegrated pair to revert to the norm.
>>>>>
>>>>> 
>>>>> Stephen Choularton Ph.D., FIoD
>>>>>
>>>>> 9999 2226
>>>>> 0413 545 182
>>>>>
>>>>>
>>>>> for insurance go to www.netinsure.com.au
>>>>> for markets go to www.organicfoodmarkets.com.au
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> [hidden email] mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>>>  Subscriberposting only. If you want to post, subscribe first.
>>>>>  Also note that this is not the rhelp list where general R questions
>>>> should go.
>>>>
>>>>
>>>>  next part 
>>>> An HTML attachment was scrubbed...
>>>> URL:<
>>>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>>>>>
>>>>  next part 
>>>> A nontext attachment was scrubbed...
>>>> Name: CoS2010Winner.JPG
>>>> Type: image/jpeg
>>>> Size: 16091 bytes
>>>> Desc: not available
>>>> URL:<
>>>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>>>>>
>>>>
>>>> 
>>>>
>>>> _______________________________________________
>>>> RSIGFinance mailing list
>>>> [hidden email]
>>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>>
>>>>
>>>> End of RSIGFinance Digest, Vol 77, Issue 8
>>>> ********************************************
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>>  Subscriberposting only. If you want to post, subscribe first.
>>>  Also note that this is not the rhelp list where general R questions should go.
>>
>>
>> 
>> Stefano M. Iacus
>> Department of Economics,
>> Business and Statistics
>> University of Milan
>> Via Conservatorio, 7
>> I20123 Milan  Italy
>> Ph.: +39 02 50321 461
>> Fax: +39 02 50321 505
>> http://www.economia.unimi.it/iacus>> 
>> Please don't send me Word or PowerPoint attachments if not
>> absolutely necessary. See:
>> http://www.gnu.org/philosophy/nowordattachments.html>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions should go.
>>
>
> 
> Patrick Burns
> [hidden email]
> http://www.burnsstat.com> http://www.portfolioprobe.com/blog>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus
Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Thanks for this help.
Trying to make sense of it so I have added some notes to the code.
I have marked them #?#
Delighted if you can tell me if I am write or wrong, add any
comments, answers.
#?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
#?# process work' particularly via dcOU
#?# I have noted in several places that I am after:
#?# 'the halflife of the decay equals ln(2)/θ'
#?# 'The halflife is given as log(2)/meanreversion speed.'
#?# and I see theta appearing at a number of points in the code.
#?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
#?# eg is one of these the theta I am after?
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
#?# random numer generation seed
set.seed(123)
#?# creation of a data set
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
#?# If I Look at X its like this:
#?# Time Series:
#?# Start = 0
#?# End = 1000
#?# Frequency = 1
#?# [1] 1.00000000 etc
#?# What sort of data object is it and how would I coerce an object with one
#?# column from a read.csv into it?
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
#?# This gives:
#?# Maximum likelihood estimation
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# Estimate Std. Error
#?# theta1 3.355322 0.28159504
#?# theta2 1.106107 0.09010627
#?# theta3 2.052815 0.07624441
#?# 2 log L: 3366.389
#?# What's this telling me?
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
#?# This provides me with this output using 'fit' from before:
#?# > vcov(fit)
#?# theta1 theta2 theta3
#?# theta1 0.07929576 0.024620718 0.016634557
#?# theta2 0.02462072 0.008119141 0.005485549
#?# theta3 0.01663456 0.005485549 0.005813209
#?# > confint(fit)
#?# Profiling...
#?# 2.5 % 97.5 %
#?# theta1 2.8448980 3.960982
#?# theta2 0.9433338 1.300629
#?# theta3 1.9147136 2.216113
#?# and 'fit' is:
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# theta1 theta2 theta3
#?# 3.355322 1.106107 2.052815
#?# plus some graphic output
#?# Again, what's this telling me.
#?# This looks like a further example?
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
Please excuse the length of this email (and my lack of understanding)
Hope you can help and thanks.
Stephen Choularton Ph.D., FIoD
On 13/10/2010 2:41 AM, stefano iacus wrote:
just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model
for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn

Message: 2
Date: Tue, 12 Oct 2010 05:43:32 0400
From: Sarbo [hidden email]
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
MessageID: [hidden email]
ContentType: text/plain; charset="utf8"
By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to
discretise the equation and then fit the data to it. I don't have the
time right now to go into all the details but it's not hard you can
parameterise the process using simple linear regression. If you need
help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the
half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions
should go.
 next part 
An HTML attachment was scrubbed...
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html
 next part 
A nontext attachment was scrubbed...
Name: CoS2010Winner.JPG
Type: image/jpeg
Size: 16091 bytes
Desc: not available
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe

_______________________________________________
RSIGFinance mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsigfinance
End of RSIGFinance Digest, Vol 77, Issue 8
********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus

Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Hi
I am still trying to sort this one out. Any comments from anyone
would be most welcome.
Stephen Choularton Ph.D., FIoD
On 14/10/2010 7:29 AM, Stephen Choularton wrote:
Thanks for this help.
Trying to make sense of it so I have added some notes to the
code. I have marked them #?#
Delighted if you can tell me if I am write or wrong, add any
comments, answers.
#?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
#?# process work' particularly via dcOU
#?# I have noted in several places that I am after:
#?# 'the halflife of the decay equals ln(2)/θ'
#?# 'The halflife is given as log(2)/meanreversion speed.'
#?# and I see theta appearing at a number of points in the code.
#?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
#?# eg is one of these the theta I am after?
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
#?# random numer generation seed
set.seed(123)
#?# creation of a data set
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
#?# If I Look at X its like this:
#?# Time Series:
#?# Start = 0
#?# End = 1000
#?# Frequency = 1
#?# [1] 1.00000000 etc
#?# What sort of data object is it and how would I coerce an object with one
#?# column from a read.csv into it?
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
#?# This gives:
#?# Maximum likelihood estimation
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# Estimate Std. Error
#?# theta1 3.355322 0.28159504
#?# theta2 1.106107 0.09010627
#?# theta3 2.052815 0.07624441
#?# 2 log L: 3366.389
#?# What's this telling me?
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
#?# This provides me with this output using 'fit' from before:
#?# > vcov(fit)
#?# theta1 theta2 theta3
#?# theta1 0.07929576 0.024620718 0.016634557
#?# theta2 0.02462072 0.008119141 0.005485549
#?# theta3 0.01663456 0.005485549 0.005813209
#?# > confint(fit)
#?# Profiling...
#?# 2.5 % 97.5 %
#?# theta1 2.8448980 3.960982
#?# theta2 0.9433338 1.300629
#?# theta3 1.9147136 2.216113
#?# and 'fit' is:
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# theta1 theta2 theta3
#?# 3.355322 1.106107 2.052815
#?# plus some graphic output
#?# Again, what's this telling me.
#?# This looks like a further example?
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
Please excuse the length of this email (and my lack of understanding)
Hope you can help and thanks.
Stephen Choularton Ph.D., FIoD
On 13/10/2010 2:41 AM, stefano iacus wrote:
just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model
for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn

Message: 2
Date: Tue, 12 Oct 2010 05:43:32 0400
From: Sarbo [hidden email]
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
MessageID: [hidden email]
ContentType: text/plain; charset="utf8"
By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to
discretise the equation and then fit the data to it. I don't have the
time right now to go into all the details but it's not hard you can
parameterise the process using simple linear regression. If you need
help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the
half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions
should go.
 next part 
An HTML attachment was scrubbed...
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html
 next part 
A nontext attachment was scrubbed...
Name: CoS2010Winner.JPG
Type: image/jpeg
Size: 16091 bytes
Desc: not available
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe

_______________________________________________
RSIGFinance mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsigfinance
End of RSIGFinance Digest, Vol 77, Issue 8
********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus

Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
Is there anyone who can give me some possible explanation or guide me to some reference? thanks
Best,
Yihao
________________________________
> Date: Tue, 19 Oct 2010 09:03:55 +1100
> From: [hidden email]
> To: [hidden email]
> CC: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>
> Hi
>
> I am still trying to sort this one out. Any comments from anyone would
> be most welcome.
>
> Stephen Choularton Ph.D., FIoD
>
>
>
> On 14/10/2010 7:29 AM, Stephen Choularton wrote:
> Thanks for this help.
>
> Trying to make sense of it so I have added some notes to the code. I
> have marked them #?#
>
> Delighted if you can tell me if I am write or wrong, add any comments,
> answers.
>
>
> #?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
> #?# process work' particularly via dcOU
> #?# I have noted in several places that I am after:
> #?# 'the halflife of the decay equals ln(2)/θ'
> #?# 'The halflife is given as log(2)/meanreversion speed.'
> #?# and I see theta appearing at a number of points in the code.
> #?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
> #?# eg is one of these the theta I am after?
>
> # ex3.01.R
> OU.lik < function(theta1, theta2, theta3){
> n < length(X)
> dt < deltat(X)
> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> }
>
> require(stats4)
> require(sde)
>
> #?# random numer generation seed
> set.seed(123)
>
> #?# creation of a data set
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> #?# If I Look at X its like this:
> #?# Time Series:
> #?# Start = 0
> #?# End = 1000
> #?# Frequency = 1
> #?# [1] 1.00000000 etc
> #?# What sort of data object is it and how would I coerce an object with one
> #?# column from a read.csv into it?
>
>
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit
> summary(fit)
>
> #?# This gives:
>
> #?# Maximum likelihood estimation
>
> #?# Call:
> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>
> #?# Coefficients:
> #?# Estimate Std. Error
> #?# theta1 3.355322 0.28159504
> #?# theta2 1.106107 0.09010627
> #?# theta3 2.052815 0.07624441
>
> #?# 2 log L: 3366.389
>
> #?# What's this telling me?
>
> # ex3.01.R (cont.)
> prof < profile(fit)
> par(mfrow=c(1,3))
> plot(prof)
> par(mfrow=c(1,1))
> vcov(fit)
> confint(fit)
>
> #?# This provides me with this output using 'fit' from before:
>
> #?# > vcov(fit)
> #?# theta1 theta2 theta3
> #?# theta1 0.07929576 0.024620718 0.016634557
> #?# theta2 0.02462072 0.008119141 0.005485549
> #?# theta3 0.01663456 0.005485549 0.005813209
> #?# > confint(fit)
> #?# Profiling...
> #?# 2.5 % 97.5 %
> #?# theta1 2.8448980 3.960982
> #?# theta2 0.9433338 1.300629
> #?# theta3 1.9147136 2.216113
>
> #?# and 'fit' is:
>
> #?# Call:
> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>
> #?# Coefficients:
> #?# theta1 theta2 theta3
> #?# 3.355322 1.106107 2.052815
>
> #?# plus some graphic output
>
> #?# Again, what's this telling me.
>
> #?# This looks like a further example?
> # ex3.01.R (cont.)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit2
> summary(fit2)
>
>
>
>
> Please excuse the length of this email (and my lack of understanding)
>
> Hope you can help and thanks.
>
>
>
>
> Stephen Choularton Ph.D., FIoD
>
>
> On 13/10/2010 2:41 AM, stefano iacus wrote:
>
> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>
> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>
> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>
>
> # ex3.01.R
> OU.lik < function(theta1, theta2, theta3){
> n < length(X)
> dt < deltat(X)
> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> }
>
> require(stats4)
> require(sde)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit
> summary(fit)
>
> # ex3.01.R (cont.)
> prof < profile(fit)
> par(mfrow=c(1,3))
> plot(prof)
> par(mfrow=c(1,1))
> vcov(fit)
> confint(fit)
>
> # ex3.01.R (cont.)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit2
> summary(fit2)
>
>
> I hope this helps out
>
> stefano
>
> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>
>
>
> Hi Stephen,
>
> You could take a look at
>
> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>
> for the linear regression method, or take a look at the package "sde" which
> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
> though, only the CIR).
>
> The halflife is given as log(2)/meanreversion speed.
>
> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
> are using (daily, yearly) for interpreting the halflife.
>
> BR,
> Bjørn
>
>
>
>
>
>
>
>
> 
>
> Message: 2
> Date: Tue, 12 Oct 2010 05:43:32 0400
> From: Sarbo
> To: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> MessageID:
> ContentType: text/plain; charset="utf8"
>
> By halflife, do you mean the speed of meanreversion?
>
> If so, there's a bit of algebraic tomfoolery that's required to
> discretise the equation and then fit the data to it. I don't have the
> time right now to go into all the details but it's not hard you can
> parameterise the process using simple linear regression. If you need
> help with that I'll try and get back to you tonight about it.
>
> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>
>
>
> Hi
>
> Wonder if anyone could point me how I use this method to discover the
> half life of a mean reverting process.
>
> I am looking into pair trading and the time it takes for a
> cointegrated pair to revert to the norm.
>
> 
> Stephen Choularton Ph.D., FIoD
>
> 9999 2226
> 0413 545 182
>
>
> for insurance go to www.netinsure.com.au
> for markets go to www.organicfoodmarkets.com.au
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions
>
>
> should go.
>
>
>  next part 
> An HTML attachment was scrubbed...
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>
>
>  next part 
> A nontext attachment was scrubbed...
> Name: CoS2010Winner.JPG
> Type: image/jpeg
> Size: 16091 bytes
> Desc: not available
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>
>
> 
>
> _______________________________________________
> RSIGFinance mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>
>
> End of RSIGFinance Digest, Vol 77, Issue 8
> ********************************************
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
> 
> Stefano M. Iacus
> Department of Economics,
> Business and Statistics
> University of Milan
> Via Conservatorio, 7
> I20123 Milan  Italy
> Ph.: +39 02 50321 461
> Fax: +39 02 50321 505
> http://www.economia.unimi.it/iacus> 
> Please don't send me Word or PowerPoint attachments if not
> absolutely necessary. See:
> http://www.gnu.org/philosophy/nowordattachments.html>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
>
>
> No virus found in this incoming message.
> Checked by AVG  www.avg.com
>
>
>
>
>
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
>
>
> No virus found in this incoming message.
> Checked by AVG  www.avg.com
>
>
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance 
> Subscriberposting only. If you want to post, subscribe first.  Also
> note that this is not the rhelp list where general R questions should
> go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Wish I could, but as you can see I am having even greater problems
;)
Stephen Choularton Ph.D., FIoD
On 19/10/2010 12:35 PM, Yihao Lu aeolus_lu wrote:
I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
Is there anyone who can give me some possible explanation or guide me to some reference? thanks
Best,
Yihao
________________________________
Date: Tue, 19 Oct 2010 09:03:55 +1100
From: [hidden email]
To: [hidden email]
CC: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
Hi
I am still trying to sort this one out. Any comments from anyone would
be most welcome.
Stephen Choularton Ph.D., FIoD
On 14/10/2010 7:29 AM, Stephen Choularton wrote:
Thanks for this help.
Trying to make sense of it so I have added some notes to the code. I
have marked them #?#
Delighted if you can tell me if I am write or wrong, add any comments,
answers.
#?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
#?# process work' particularly via dcOU
#?# I have noted in several places that I am after:
#?# 'the halflife of the decay equals ln(2)/θ'
#?# 'The halflife is given as log(2)/meanreversion speed.'
#?# and I see theta appearing at a number of points in the code.
#?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
#?# eg is one of these the theta I am after?
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
#?# random numer generation seed
set.seed(123)
#?# creation of a data set
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
#?# If I Look at X its like this:
#?# Time Series:
#?# Start = 0
#?# End = 1000
#?# Frequency = 1
#?# [1] 1.00000000 etc
#?# What sort of data object is it and how would I coerce an object with one
#?# column from a read.csv into it?
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
#?# This gives:
#?# Maximum likelihood estimation
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# Estimate Std. Error
#?# theta1 3.355322 0.28159504
#?# theta2 1.106107 0.09010627
#?# theta3 2.052815 0.07624441
#?# 2 log L: 3366.389
#?# What's this telling me?
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
#?# This provides me with this output using 'fit' from before:
#?# > vcov(fit)
#?# theta1 theta2 theta3
#?# theta1 0.07929576 0.024620718 0.016634557
#?# theta2 0.02462072 0.008119141 0.005485549
#?# theta3 0.01663456 0.005485549 0.005813209
#?# > confint(fit)
#?# Profiling...
#?# 2.5 % 97.5 %
#?# theta1 2.8448980 3.960982
#?# theta2 0.9433338 1.300629
#?# theta3 1.9147136 2.216113
#?# and 'fit' is:
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# theta1 theta2 theta3
#?# 3.355322 1.106107 2.052815
#?# plus some graphic output
#?# Again, what's this telling me.
#?# This looks like a further example?
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
Please excuse the length of this email (and my lack of understanding)
Hope you can help and thanks.
Stephen Choularton Ph.D., FIoD
On 13/10/2010 2:41 AM, stefano iacus wrote:
just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model
for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn

Message: 2
Date: Tue, 12 Oct 2010 05:43:32 0400
From: Sarbo
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
MessageID:
ContentType: text/plain; charset="utf8"
By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to
discretise the equation and then fit the data to it. I don't have the
time right now to go into all the details but it's not hard you can
parameterise the process using simple linear regression. If you need
help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the
half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions
should go.
 next part 
An HTML attachment was scrubbed...
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html
 next part 
A nontext attachment was scrubbed...
Name: CoS2010Winner.JPG
Type: image/jpeg
Size: 16091 bytes
Desc: not available
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe

_______________________________________________
RSIGFinance mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsigfinance
End of RSIGFinance Digest, Vol 77, Issue 8
********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus

Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance 
Subscriberposting only. If you want to post, subscribe first.  Also
note that this is not the rhelp list where general R questions should
go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


regarding your problem, i think Bjorn's link is very helpful. it even has the matlab code attached. several lines, you can translate it into R and do a comparison on the data, you will have the idea which theta is the rate you should look at.
Best,
Yihao
________________________________
> Date: Tue, 19 Oct 2010 12:50:46 +1100
> From: [hidden email]
> To: [hidden email]
> CC: [hidden email]
> Subject: Re: [RSIGFinance] Mean reversion
>
> Wish I could, but as you can see I am having even greater problems ;)
>
> Stephen Choularton Ph.D., FIoD
>
> On 19/10/2010 12:35 PM, Yihao Lu aeolus_lu wrote:
>
>
> I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
> Is there anyone who can give me some possible explanation or guide me to some reference? thanks
>
> Best,
> Yihao
>
>
>
>
>
>
>
> ________________________________
>
>
> Date: Tue, 19 Oct 2010 09:03:55 +1100
> From: [hidden email]
> To: [hidden email]
> CC: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>
> Hi
>
> I am still trying to sort this one out. Any comments from anyone would
> be most welcome.
>
> Stephen Choularton Ph.D., FIoD
>
>
>
> On 14/10/2010 7:29 AM, Stephen Choularton wrote:
> Thanks for this help.
>
> Trying to make sense of it so I have added some notes to the code. I
> have marked them #?#
>
> Delighted if you can tell me if I am write or wrong, add any comments,
> answers.
>
>
> #?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
> #?# process work' particularly via dcOU
> #?# I have noted in several places that I am after:
> #?# 'the halflife of the decay equals ln(2)/θ'
> #?# 'The halflife is given as log(2)/meanreversion speed.'
> #?# and I see theta appearing at a number of points in the code.
> #?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
> #?# eg is one of these the theta I am after?
>
> # ex3.01.R
> OU.lik < function(theta1, theta2, theta3){
> n < length(X)
> dt < deltat(X)
> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> }
>
> require(stats4)
> require(sde)
>
> #?# random numer generation seed
> set.seed(123)
>
> #?# creation of a data set
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> #?# If I Look at X its like this:
> #?# Time Series:
> #?# Start = 0
> #?# End = 1000
> #?# Frequency = 1
> #?# [1] 1.00000000 etc
> #?# What sort of data object is it and how would I coerce an object with one
> #?# column from a read.csv into it?
>
>
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit
> summary(fit)
>
> #?# This gives:
>
> #?# Maximum likelihood estimation
>
> #?# Call:
> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>
> #?# Coefficients:
> #?# Estimate Std. Error
> #?# theta1 3.355322 0.28159504
> #?# theta2 1.106107 0.09010627
> #?# theta3 2.052815 0.07624441
>
> #?# 2 log L: 3366.389
>
> #?# What's this telling me?
>
> # ex3.01.R (cont.)
> prof < profile(fit)
> par(mfrow=c(1,3))
> plot(prof)
> par(mfrow=c(1,1))
> vcov(fit)
> confint(fit)
>
> #?# This provides me with this output using 'fit' from before:
>
> #?# > vcov(fit)
> #?# theta1 theta2 theta3
> #?# theta1 0.07929576 0.024620718 0.016634557
> #?# theta2 0.02462072 0.008119141 0.005485549
> #?# theta3 0.01663456 0.005485549 0.005813209
> #?# > confint(fit)
> #?# Profiling...
> #?# 2.5 % 97.5 %
> #?# theta1 2.8448980 3.960982
> #?# theta2 0.9433338 1.300629
> #?# theta3 1.9147136 2.216113
>
> #?# and 'fit' is:
>
> #?# Call:
> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>
> #?# Coefficients:
> #?# theta1 theta2 theta3
> #?# 3.355322 1.106107 2.052815
>
> #?# plus some graphic output
>
> #?# Again, what's this telling me.
>
> #?# This looks like a further example?
> # ex3.01.R (cont.)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit2
> summary(fit2)
>
>
>
>
> Please excuse the length of this email (and my lack of understanding)
>
> Hope you can help and thanks.
>
>
>
>
> Stephen Choularton Ph.D., FIoD
>
>
> On 13/10/2010 2:41 AM, stefano iacus wrote:
>
> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>
> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>
> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>
>
> # ex3.01.R
> OU.lik < function(theta1, theta2, theta3){
> n < length(X)
> dt < deltat(X)
> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> }
>
> require(stats4)
> require(sde)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit
> summary(fit)
>
> # ex3.01.R (cont.)
> prof < profile(fit)
> par(mfrow=c(1,3))
> plot(prof)
> par(mfrow=c(1,1))
> vcov(fit)
> confint(fit)
>
> # ex3.01.R (cont.)
> set.seed(123)
> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> method="LBFGSB", lower=c(Inf,0,0)) > fit2
> summary(fit2)
>
>
> I hope this helps out
>
> stefano
>
> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>
>
>
> Hi Stephen,
>
> You could take a look at
>
> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>
> for the linear regression method, or take a look at the package "sde" which
> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
> though, only the CIR).
>
> The halflife is given as log(2)/meanreversion speed.
>
> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
> are using (daily, yearly) for interpreting the halflife.
>
> BR,
> Bjørn
>
>
>
>
>
>
>
>
> 
>
> Message: 2
> Date: Tue, 12 Oct 2010 05:43:32 0400
> From: Sarbo
> To: [hidden email]
> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> MessageID:
> ContentType: text/plain; charset="utf8"
>
> By halflife, do you mean the speed of meanreversion?
>
> If so, there's a bit of algebraic tomfoolery that's required to
> discretise the equation and then fit the data to it. I don't have the
> time right now to go into all the details but it's not hard you can
> parameterise the process using simple linear regression. If you need
> help with that I'll try and get back to you tonight about it.
>
> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>
>
>
> Hi
>
> Wonder if anyone could point me how I use this method to discover the
> half life of a mean reverting process.
>
> I am looking into pair trading and the time it takes for a
> cointegrated pair to revert to the norm.
>
> 
> Stephen Choularton Ph.D., FIoD
>
> 9999 2226
> 0413 545 182
>
>
> for insurance go to www.netinsure.com.au
> for markets go to www.organicfoodmarkets.com.au
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions
>
>
> should go.
>
>
>  next part 
> An HTML attachment was scrubbed...
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>
>
>  next part 
> A nontext attachment was scrubbed...
> Name: CoS2010Winner.JPG
> Type: image/jpeg
> Size: 16091 bytes
> Desc: not available
> URL: <
> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>
>
> 
>
> _______________________________________________
> RSIGFinance mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>
>
> End of RSIGFinance Digest, Vol 77, Issue 8
> ********************************************
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
> 
> Stefano M. Iacus
> Department of Economics,
> Business and Statistics
> University of Milan
> Via Conservatorio, 7
> I20123 Milan  Italy
> Ph.: +39 02 50321 461
> Fax: +39 02 50321 505
> http://www.economia.unimi.it/iacus> 
> Please don't send me Word or PowerPoint attachments if not
> absolutely necessary. See:
> http://www.gnu.org/philosophy/nowordattachments.html>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
>
>
> No virus found in this incoming message.
> Checked by AVG  www.avg.com
>
>
>
>
>
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
>
>
> No virus found in this incoming message.
> Checked by AVG  www.avg.com
>
>
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance 
> Subscriberposting only. If you want to post, subscribe first.  Also
> note that this is not the rhelp list where general R questions should
> go.
>
>
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
>
>
>
>
>
> No virus found in this incoming message.
> Checked by AVG  www.avg.com
> Version: 9.0.862 / Virus Database: 271.1.1/3204  Release Date: 10/18/10 17:34:00
>
>
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Hi Folks
I'm using this to find cointegrated stocks on the AX.
library(xts)
library(quantmod)
# quickly resource this file
s < function() source('meanrev.R')
checkPairFromYahoo < function(sym1, sym2, dateFilter='::')
{
t.xts < getCombined(sym1, sym2, dateFilter=dateFilter)
cat("Date range is", format(start(t.xts)), "to",
format(end(t.xts)), "\n")
# Build linear model
m < buildLM(t.xts)
# Note beta  http://en.wikipedia.org/wiki/Beta_(finance)
beta < getBeta(m)
cat("Assumed hedge ratio is", beta, "\n")
# Build spread
sprd < buildSpread(t.xts, beta)
# Test cointegration
ht < testCoint(sprd)
cat("PP pvalue is", as.double(ht$p.value), "\n")
if (as.double(ht$p.value) < 0.05)
{
cat("###############################################################\n",
sym1 ,":", sym2 ," is likely meanreverting.\n",
"###########################################################\n" )
}
else
{
#cat(sym1 ,":", sym2 ," is not meanreverting.\n")
}
}
getCombined < function(sym1, sym2, dateFilter='::')
{
# Grab historical data for both symbols
one < getSymbols(sym1, auto.assign=FALSE)
two < getSymbols(sym2, auto.assign=FALSE)
# Give columns more usable names
colnames(one) < c('Open', 'High', 'Low', 'Close', 'Volume',
'Adjusted')
colnames(two) < c('Open', 'High', 'Low', 'Close', 'Volume',
'Adjusted')
# Build combined object
return(merge(one$Close, two$Close, all=FALSE)[dateFilter])
}
buildLM < function(combined)
{
return(lm(Close ~ Close.1 + 0, combined))
}
getBeta < function(m)
{
return(as.double(coef(m)[1]))
}
buildSpread < function(combined, beta)
{
return(combined$Close  beta*combined$Close.1)
}
testCoint < function(sprd)
{
return(PP.test(sprd, lshort = FALSE))
}
I run it on batches of stockpairs and then have a look at those
which are cointegrated. Assuming my code is right (and anyone who
thinks there is something wrong with it please let me know ;)
Just wondered if anyone simply goes with the results, or if a test
of logic is required. I found, for example, that AGL ( a big gas
company) was cointegrated with Bunnings Wharehouses (a hardware
superstore chain). Can't see the reason for that. AMP (major
insurer) cointegrates with AXA (another major insurer). That makes
sense and it cointegrates with Westpac (major bank) still some
logic but a bit thinner. It also cointegrates with Fortescue Metals
(big iron ore operation). Not much logic there. Anyway question
is: do you get better results by using informed judgement on these
things or just trust the figures?
Any comments most welcome.
On 19/10/2010 12:35 PM, Yihao Lu aeolus_lu wrote:
I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
Is there anyone who can give me some possible explanation or guide me to some reference? thanks
Best,
Yihao
________________________________
Date: Tue, 19 Oct 2010 09:03:55 +1100
From: [hidden email]
To: [hidden email]
CC: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
Hi
I am still trying to sort this one out. Any comments from anyone would
be most welcome.
Stephen Choularton Ph.D., FIoD
On 14/10/2010 7:29 AM, Stephen Choularton wrote:
Thanks for this help.
Trying to make sense of it so I have added some notes to the code. I
have marked them #?#
Delighted if you can tell me if I am write or wrong, add any comments,
answers.
#?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
#?# process work' particularly via dcOU
#?# I have noted in several places that I am after:
#?# 'the halflife of the decay equals ln(2)/θ'
#?# 'The halflife is given as log(2)/meanreversion speed.'
#?# and I see theta appearing at a number of points in the code.
#?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
#?# eg is one of these the theta I am after?
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
#?# random numer generation seed
set.seed(123)
#?# creation of a data set
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
#?# If I Look at X its like this:
#?# Time Series:
#?# Start = 0
#?# End = 1000
#?# Frequency = 1
#?# [1] 1.00000000 etc
#?# What sort of data object is it and how would I coerce an object with one
#?# column from a read.csv into it?
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
#?# This gives:
#?# Maximum likelihood estimation
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# Estimate Std. Error
#?# theta1 3.355322 0.28159504
#?# theta2 1.106107 0.09010627
#?# theta3 2.052815 0.07624441
#?# 2 log L: 3366.389
#?# What's this telling me?
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
#?# This provides me with this output using 'fit' from before:
#?# > vcov(fit)
#?# theta1 theta2 theta3
#?# theta1 0.07929576 0.024620718 0.016634557
#?# theta2 0.02462072 0.008119141 0.005485549
#?# theta3 0.01663456 0.005485549 0.005813209
#?# > confint(fit)
#?# Profiling...
#?# 2.5 % 97.5 %
#?# theta1 2.8448980 3.960982
#?# theta2 0.9433338 1.300629
#?# theta3 1.9147136 2.216113
#?# and 'fit' is:
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# theta1 theta2 theta3
#?# 3.355322 1.106107 2.052815
#?# plus some graphic output
#?# Again, what's this telling me.
#?# This looks like a further example?
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
Please excuse the length of this email (and my lack of understanding)
Hope you can help and thanks.
Stephen Choularton Ph.D., FIoD
On 13/10/2010 2:41 AM, stefano iacus wrote:
just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model
for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn

Message: 2
Date: Tue, 12 Oct 2010 05:43:32 0400
From: Sarbo
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
MessageID:
ContentType: text/plain; charset="utf8"
By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to
discretise the equation and then fit the data to it. I don't have the
time right now to go into all the details but it's not hard you can
parameterise the process using simple linear regression. If you need
help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the
half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions
should go.
 next part 
An HTML attachment was scrubbed...
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html
 next part 
A nontext attachment was scrubbed...
Name: CoS2010Winner.JPG
Type: image/jpeg
Size: 16091 bytes
Desc: not available
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe

_______________________________________________
RSIGFinance mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsigfinance
End of RSIGFinance Digest, Vol 77, Issue 8
********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus

Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance 
Subscriberposting only. If you want to post, subscribe first.  Also
note that this is not the rhelp list where general R questions should
go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


You have to be careful when interpreting rolling ADF tests because the usual critical values for evaluating the tests are not valid. See the 1992 Journal of Business and Economic Statistics paper by Banerjee, Lumsdaine and Stock.
****************************************************************
* Eric Zivot *
* Professor and Gary Waterman Distinguished Scholar *
* Department of Economics *
* Adjunct Professor of Finance *
* Adjunct Professor of Statistics
* Box 353330 email: [hidden email] *
* University of Washington phone: 2065436715 *
* Seattle, WA 981953330 * *
* www: http://faculty.washington.edu/ezivot *
****************************************************************
On Mon, 18 Oct 2010, Yihao Lu aeolus_lu wrote:
>
> I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
> Is there anyone who can give me some possible explanation or guide me to some reference? thanks
>
> Best,
> Yihao
>
>
>
>
>
>
>
> ________________________________
>> Date: Tue, 19 Oct 2010 09:03:55 +1100
>> From: [hidden email]
>> To: [hidden email]
>> CC: [hidden email]
>> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>>
>> Hi
>>
>> I am still trying to sort this one out. Any comments from anyone would
>> be most welcome.
>>
>> Stephen Choularton Ph.D., FIoD
>>
>>
>>
>> On 14/10/2010 7:29 AM, Stephen Choularton wrote:
>> Thanks for this help.
>>
>> Trying to make sense of it so I have added some notes to the code. I
>> have marked them #?#
>>
>> Delighted if you can tell me if I am write or wrong, add any comments,
>> answers.
>>
>>
>> #?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
>> #?# process work' particularly via dcOU
>> #?# I have noted in several places that I am after:
>> #?# 'the halflife of the decay equals ln(2)/θ'
>> #?# 'The halflife is given as log(2)/meanreversion speed.'
>> #?# and I see theta appearing at a number of points in the code.
>> #?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
>> #?# eg is one of these the theta I am after?
>>
>> # ex3.01.R
>> OU.lik < function(theta1, theta2, theta3){
>> n < length(X)
>> dt < deltat(X)
>> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
>> }
>>
>> require(stats4)
>> require(sde)
>>
>> #?# random numer generation seed
>> set.seed(123)
>>
>> #?# creation of a data set
>> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
>> #?# If I Look at X its like this:
>> #?# Time Series:
>> #?# Start = 0
>> #?# End = 1000
>> #?# Frequency = 1
>> #?# [1] 1.00000000 etc
>> #?# What sort of data object is it and how would I coerce an object with one
>> #?# column from a read.csv into it?
>>
>>
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit
>> summary(fit)
>>
>> #?# This gives:
>>
>> #?# Maximum likelihood estimation
>>
>> #?# Call:
>> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
>> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>>
>> #?# Coefficients:
>> #?# Estimate Std. Error
>> #?# theta1 3.355322 0.28159504
>> #?# theta2 1.106107 0.09010627
>> #?# theta3 2.052815 0.07624441
>>
>> #?# 2 log L: 3366.389
>>
>> #?# What's this telling me?
>>
>> # ex3.01.R (cont.)
>> prof < profile(fit)
>> par(mfrow=c(1,3))
>> plot(prof)
>> par(mfrow=c(1,1))
>> vcov(fit)
>> confint(fit)
>>
>> #?# This provides me with this output using 'fit' from before:
>>
>> #?# > vcov(fit)
>> #?# theta1 theta2 theta3
>> #?# theta1 0.07929576 0.024620718 0.016634557
>> #?# theta2 0.02462072 0.008119141 0.005485549
>> #?# theta3 0.01663456 0.005485549 0.005813209
>> #?# > confint(fit)
>> #?# Profiling...
>> #?# 2.5 % 97.5 %
>> #?# theta1 2.8448980 3.960982
>> #?# theta2 0.9433338 1.300629
>> #?# theta3 1.9147136 2.216113
>>
>> #?# and 'fit' is:
>>
>> #?# Call:
>> #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
>> #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
>>
>> #?# Coefficients:
>> #?# theta1 theta2 theta3
>> #?# 3.355322 1.106107 2.052815
>>
>> #?# plus some graphic output
>>
>> #?# Again, what's this telling me.
>>
>> #?# This looks like a further example?
>> # ex3.01.R (cont.)
>> set.seed(123)
>> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit2
>> summary(fit2)
>>
>>
>>
>>
>> Please excuse the length of this email (and my lack of understanding)
>>
>> Hope you can help and thanks.
>>
>>
>>
>>
>> Stephen Choularton Ph.D., FIoD
>>
>>
>> On 13/10/2010 2:41 AM, stefano iacus wrote:
>>
>> just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
>>
>> sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
>>
>> This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
>>
>>
>> # ex3.01.R
>> OU.lik < function(theta1, theta2, theta3){
>> n < length(X)
>> dt < deltat(X)
>> sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
>> }
>>
>> require(stats4)
>> require(sde)
>> set.seed(123)
>> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit
>> summary(fit)
>>
>> # ex3.01.R (cont.)
>> prof < profile(fit)
>> par(mfrow=c(1,3))
>> plot(prof)
>> par(mfrow=c(1,1))
>> vcov(fit)
>> confint(fit)
>>
>> # ex3.01.R (cont.)
>> set.seed(123)
>> X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
>> mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
>> method="LBFGSB", lower=c(Inf,0,0)) > fit2
>> summary(fit2)
>>
>>
>> I hope this helps out
>>
>> stefano
>>
>> On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
>>
>>
>>
>> Hi Stephen,
>>
>> You could take a look at
>>
>> http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model>>
>> for the linear regression method, or take a look at the package "sde" which
>> contains some examples using GMM (not for the OrnsteinUhlenbeck process,
>> though, only the CIR).
>>
>> The halflife is given as log(2)/meanreversion speed.
>>
>> Do keep an eye on the partition of the timeaxis, e.g. what frequency you
>> are using (daily, yearly) for interpreting the halflife.
>>
>> BR,
>> Bjørn
>>
>>
>>
>>
>>
>>
>>
>>
>> 
>>
>> Message: 2
>> Date: Tue, 12 Oct 2010 05:43:32 0400
>> From: Sarbo
>> To: [hidden email]
>> Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
>> MessageID:
>> ContentType: text/plain; charset="utf8"
>>
>> By halflife, do you mean the speed of meanreversion?
>>
>> If so, there's a bit of algebraic tomfoolery that's required to
>> discretise the equation and then fit the data to it. I don't have the
>> time right now to go into all the details but it's not hard you can
>> parameterise the process using simple linear regression. If you need
>> help with that I'll try and get back to you tonight about it.
>>
>> On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
>>
>>
>>
>> Hi
>>
>> Wonder if anyone could point me how I use this method to discover the
>> half life of a mean reverting process.
>>
>> I am looking into pair trading and the time it takes for a
>> cointegrated pair to revert to the norm.
>>
>> 
>> Stephen Choularton Ph.D., FIoD
>>
>> 9999 2226
>> 0413 545 182
>>
>>
>> for insurance go to www.netinsure.com.au
>> for markets go to www.organicfoodmarkets.com.au
>>
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions
>>
>>
>> should go.
>>
>>
>>  next part 
>> An HTML attachment was scrubbed...
>> URL: <
>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html>>
>>
>>  next part 
>> A nontext attachment was scrubbed...
>> Name: CoS2010Winner.JPG
>> Type: image/jpeg
>> Size: 16091 bytes
>> Desc: not available
>> URL: <
>> https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe>>
>>
>> 
>>
>> _______________________________________________
>> RSIGFinance mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>
>>
>> End of RSIGFinance Digest, Vol 77, Issue 8
>> ********************************************
>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions should go.
>>
>>
>>
>> 
>> Stefano M. Iacus
>> Department of Economics,
>> Business and Statistics
>> University of Milan
>> Via Conservatorio, 7
>> I20123 Milan  Italy
>> Ph.: +39 02 50321 461
>> Fax: +39 02 50321 505
>> http://www.economia.unimi.it/iacus>> 
>> Please don't send me Word or PowerPoint attachments if not
>> absolutely necessary. See:
>> http://www.gnu.org/philosophy/nowordattachments.html>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions should go.
>>
>>
>>
>>
>>
>> No virus found in this incoming message.
>> Checked by AVG  www.avg.com
>>
>>
>>
>>
>>
>>
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance>>  Subscriberposting only. If you want to post, subscribe first.
>>  Also note that this is not the rhelp list where general R questions should go.
>>
>>
>>
>>
>>
>> No virus found in this incoming message.
>> Checked by AVG  www.avg.com
>>
>>
>>
>>
>> _______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/rsigfinance 
>> Subscriberposting only. If you want to post, subscribe first.  Also
>> note that this is not the rhelp list where general R questions should
>> go.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Yihao,
Prof. Zivot is right. The ADF test isn't a great way to test for
meanreversion; it's merely a way to test for stationarity to specify
the degrees in an ARIMA model.
I dug up some code from my misspent youth as a consultant which you
might find useful:
StochasticProcessTest < function(PriceSeries, delta.t, p.value,
diagnostics = TRUE, from = NULL, to = NULL,
by = NULL, currency = '($)'){
require(stats)
require(fSeries)
m < length(PriceSeries)
S1 < PriceSeries[1:(m1)]
S2 < PriceSeries[2:m]
#Fit a GBM process:
Y < diff(log(PriceSeries)); X < S1
GBMfit < lm(Y ~ X)
#Fit a meanreverting GBM process:
Y < diff(PriceSeries) / S1; X < log(S1)
MRGBMfit < lm(Y ~ X)
#Fit a Vasicek (OU) process:
Y < diff(PriceSeries); X < S1
Vfit < lm(Y ~ X)
#Fit a CoxIngersollRoss process:
Y < diff(PriceSeries) / sqrt(S1); X < S1 / sqrt(S1)
CIRfit < lm(Y ~ X)
#Gather the parameter estimates:
kappa < as.vector((c(0, MRGBMfit$coef[2], Vfit$coef[2], CIRfit
$coef[2])) / delta.t)
mu < as.vector((c(mean(log(S2/S1)), MRGBMfit$coef[1] / kappa[2], Vfit
$coef[1] / kappa[3],
CIRfit$coef[1] / kappa[4])) / delta.t)
sigma < (c(sd(GBMfit$resid), sd(MRGBMfit$resid), sd(Vfit$resid),
sd(CIRfit$resid))) / sqrt(delta.t)
tstat < as.vector(c(summary(GBMfit)$coef[2,3],
summary(MRGBMfit)$coef[2,3], summary(Vfit)$coef[2,3],
summary(CIRfit)$coef[2,3]))
fstat < list(summary(GBMfit)$fstatistic,
summary(MRGBMfit)$fstatistic, summary(Vfit)$fstatistic,
summary(CIRfit)$fstatistic)
names(fstat) < c('GBM', 'Mean.Revert.GBM', 'Vasicek', 'CIR')
AICs < c(AIC(GBMfit), AIC(MRGBMfit), AIC(Vfit), AIC(CIRfit))
paramframe < data.frame(rbind(kappa, mu, sigma, tstat, AICs))
names(paramframe) < names(fstat)
#Now figure out what the actual process is, using AIC:
crit < ifelse(m > 30, qnorm(1  p.value), qt(1  p.value, df = n))
tmp < which.min(AICs)
Processes < names(fstat)
Verdict < Processes[tmp]
FinalSummary < switch(Verdict, GBM = summary(GBMfit), CIR =
summary(CIRfit), Mean.Revert.GBM = MRGBMfit,
Vasicek = Vfit)
fitobj < switch(Verdict, GBM = GBMfit, CIR = CIRfit, Mean.Revert.GBM
= MRGBMfit, Vasicek = Vfit)
Output < list(Parameters = paramframe, Critical.Value = crit, Verdict
= Verdict, FinalSummary = FinalSummary,
fstat = fstat, fitted.object = fitobj)
if (diagnostics){
op < par(ask = TRUE)
on.exit(op)
if(!all(c(class(from), class(to)) == 'Date')){
S < timeSeries(PriceSeries)
} else S = timeSeries(PriceSeries, seq(from, to, length.out = m))
plot(S, type = 'l', xlab = 'Date', ylab = paste('Price Series',
currency), main = 'Time Series Plot of Data',
lwd = 2, col = 'blue')
rets < returns(PriceSeries, 'continuous')[1]
hist(rets, xlab = paste('LogReturns', currency), col = 'blue',
border = 'white', main = 'Histogram of Return Series',
freq = FALSE)
x < seq(min(rets), max(rets), length.out = max(m, 1000))
lines(x, dnorm(x, mean(rets), sd(rets)), col = 'magenta', lwd = 2)
lines(density(rets), col = 'green', lwd = 2)
legend('topright', legend = c('LogReturns', 'Observed CDF',
'Gaussian Fit'), lwd = rep(2, 3),
col = c('blue', 'green', 'magenta'))
plot(fitobj, 1:6)
}
return(Output)
}
(I don't claim that it's necessarily great code, but it does seem to
work.)
On Mon, 20101018 at 21:35 0400, Yihao Lu aeolus_lu wrote:
> I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
> Is there anyone who can give me some possible explanation or guide me to some reference? thanks
>
> Best,
> Yihao
>
>
>
>
>
>
>
> ________________________________
> > Date: Tue, 19 Oct 2010 09:03:55 +1100
> > From: [hidden email]
> > To: [hidden email]
> > CC: [hidden email]
> > Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> >
> > Hi
> >
> > I am still trying to sort this one out. Any comments from anyone would
> > be most welcome.
> >
> > Stephen Choularton Ph.D., FIoD
> >
> >
> >
> > On 14/10/2010 7:29 AM, Stephen Choularton wrote:
> > Thanks for this help.
> >
> > Trying to make sense of it so I have added some notes to the code. I
> > have marked them #?#
> >
> > Delighted if you can tell me if I am write or wrong, add any comments,
> > answers.
> >
> >
> > #?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
> > #?# process work' particularly via dcOU
> > #?# I have noted in several places that I am after:
> > #?# 'the halflife of the decay equals ln(2)/Î¸'
> > #?# 'The halflife is given as log(2)/meanreversion speed.'
> > #?# and I see theta appearing at a number of points in the code.
> > #?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
> > #?# eg is one of these the theta I am after?
> >
> > # ex3.01.R
> > OU.lik < function(theta1, theta2, theta3){
> > n < length(X)
> > dt < deltat(X)
> > sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> > }
> >
> > require(stats4)
> > require(sde)
> >
> > #?# random numer generation seed
> > set.seed(123)
> >
> > #?# creation of a data set
> > X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> > #?# If I Look at X its like this:
> > #?# Time Series:
> > #?# Start = 0
> > #?# End = 1000
> > #?# Frequency = 1
> > #?# [1] 1.00000000 etc
> > #?# What sort of data object is it and how would I coerce an object with one
> > #?# column from a read.csv into it?
> >
> >
> > mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> > method="LBFGSB", lower=c(Inf,0,0)) > fit
> > summary(fit)
> >
> > #?# This gives:
> >
> > #?# Maximum likelihood estimation
> >
> > #?# Call:
> > #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> > #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
> >
> > #?# Coefficients:
> > #?# Estimate Std. Error
> > #?# theta1 3.355322 0.28159504
> > #?# theta2 1.106107 0.09010627
> > #?# theta3 2.052815 0.07624441
> >
> > #?# 2 log L: 3366.389
> >
> > #?# What's this telling me?
> >
> > # ex3.01.R (cont.)
> > prof < profile(fit)
> > par(mfrow=c(1,3))
> > plot(prof)
> > par(mfrow=c(1,1))
> > vcov(fit)
> > confint(fit)
> >
> > #?# This provides me with this output using 'fit' from before:
> >
> > #?# > vcov(fit)
> > #?# theta1 theta2 theta3
> > #?# theta1 0.07929576 0.024620718 0.016634557
> > #?# theta2 0.02462072 0.008119141 0.005485549
> > #?# theta3 0.01663456 0.005485549 0.005813209
> > #?# > confint(fit)
> > #?# Profiling...
> > #?# 2.5 % 97.5 %
> > #?# theta1 2.8448980 3.960982
> > #?# theta2 0.9433338 1.300629
> > #?# theta3 1.9147136 2.216113
> >
> > #?# and 'fit' is:
> >
> > #?# Call:
> > #?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
> > #?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
> >
> > #?# Coefficients:
> > #?# theta1 theta2 theta3
> > #?# 3.355322 1.106107 2.052815
> >
> > #?# plus some graphic output
> >
> > #?# Again, what's this telling me.
> >
> > #?# This looks like a further example?
> > # ex3.01.R (cont.)
> > set.seed(123)
> > X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> > mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> > method="LBFGSB", lower=c(Inf,0,0)) > fit2
> > summary(fit2)
> >
> >
> >
> >
> > Please excuse the length of this email (and my lack of understanding)
> >
> > Hope you can help and thanks.
> >
> >
> >
> >
> > Stephen Choularton Ph.D., FIoD
> >
> >
> > On 13/10/2010 2:41 AM, stefano iacus wrote:
> >
> > just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
> >
> > sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
> >
> > This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
> >
> >
> > # ex3.01.R
> > OU.lik < function(theta1, theta2, theta3){
> > n < length(X)
> > dt < deltat(X)
> > sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
> > }
> >
> > require(stats4)
> > require(sde)
> > set.seed(123)
> > X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
> > mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> > method="LBFGSB", lower=c(Inf,0,0)) > fit
> > summary(fit)
> >
> > # ex3.01.R (cont.)
> > prof < profile(fit)
> > par(mfrow=c(1,3))
> > plot(prof)
> > par(mfrow=c(1,1))
> > vcov(fit)
> > confint(fit)
> >
> > # ex3.01.R (cont.)
> > set.seed(123)
> > X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
> > mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
> > method="LBFGSB", lower=c(Inf,0,0)) > fit2
> > summary(fit2)
> >
> >
> > I hope this helps out
> >
> > stefano
> >
> > On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
> >
> >
> >
> > Hi Stephen,
> >
> > You could take a look at
> >
> > http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model> >
> > for the linear regression method, or take a look at the package "sde" which
> > contains some examples using GMM (not for the OrnsteinUhlenbeck process,
> > though, only the CIR).
> >
> > The halflife is given as log(2)/meanreversion speed.
> >
> > Do keep an eye on the partition of the timeaxis, e.g. what frequency you
> > are using (daily, yearly) for interpreting the halflife.
> >
> > BR,
> > BjÃ¸rn
> >
> >
> >
> >
> >
> >
> >
> >
> > 
> >
> > Message: 2
> > Date: Tue, 12 Oct 2010 05:43:32 0400
> > From: Sarbo
> > To: [hidden email]
> > Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
> > MessageID:
> > ContentType: text/plain; charset="utf8"
> >
> > By halflife, do you mean the speed of meanreversion?
> >
> > If so, there's a bit of algebraic tomfoolery that's required to
> > discretise the equation and then fit the data to it. I don't have the
> > time right now to go into all the details but it's not hard you can
> > parameterise the process using simple linear regression. If you need
> > help with that I'll try and get back to you tonight about it.
> >
> > On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
> >
> >
> >
> > Hi
> >
> > Wonder if anyone could point me how I use this method to discover the
> > half life of a mean reverting process.
> >
> > I am looking into pair trading and the time it takes for a
> > cointegrated pair to revert to the norm.
> >
> > 
> > Stephen Choularton Ph.D., FIoD
> >
> > 9999 2226
> > 0413 545 182
> >
> >
> > for insurance go to www.netinsure.com.au
> > for markets go to www.organicfoodmarkets.com.au
> >
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R questions
> >
> >
> > should go.
> >
> >
> >  next part 
> > An HTML attachment was scrubbed...
> > URL: <
> > https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html> >
> >
> >  next part 
> > A nontext attachment was scrubbed...
> > Name: CoS2010Winner.JPG
> > Type: image/jpeg
> > Size: 16091 bytes
> > Desc: not available
> > URL: <
> > https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe> >
> >
> > 
> >
> > _______________________________________________
> > RSIGFinance mailing list
> > [hidden email]
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >
> >
> > End of RSIGFinance Digest, Vol 77, Issue 8
> > ********************************************
> >
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R questions should go.
> >
> >
> >
> > 
> > Stefano M. Iacus
> > Department of Economics,
> > Business and Statistics
> > University of Milan
> > Via Conservatorio, 7
> > I20123 Milan  Italy
> > Ph.: +39 02 50321 461
> > Fax: +39 02 50321 505
> > http://www.economia.unimi.it/iacus> > 
> > Please don't send me Word or PowerPoint attachments if not
> > absolutely necessary. See:
> > http://www.gnu.org/philosophy/nowordattachments.html> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R questions should go.
> >
> >
> >
> >
> >
> > No virus found in this incoming message.
> > Checked by AVG  www.avg.com
> >
> >
> >
> >
> >
> >
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance> >  Subscriberposting only. If you want to post, subscribe first.
> >  Also note that this is not the rhelp list where general R questions should go.
> >
> >
> >
> >
> >
> > No virus found in this incoming message.
> > Checked by AVG  www.avg.com
> >
> >
> >
> >
> > _______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/rsigfinance 
> > Subscriberposting only. If you want to post, subscribe first.  Also
> > note that this is not the rhelp list where general R questions should
> > go.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/rsigfinance>  Subscriberposting only. If you want to post, subscribe first.
>  Also note that this is not the rhelp list where general R questions should go.
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


In reply to this post by Stephen Choularton3
Stephen,
It depends what you mean by "logic".
If you mean statistical logic, I'll defer to Eric Zivot and
Sarbo who are far wiser than I am. I will note, however, that you are testing
for a pvalue of 0.05, so I expect 5% of your test results to be misleading. In
other words, for every 20 pairs tested by your batch job, I expect one will be
suspect.
"Spurious cointegration" is a serious problem. I suggest
Googling that topic. You may be suprised what you learn. (The irony, of course,
is that cointegration was supposed to cure "spurious correlation." Oh
well.)
If you mean financial logic, I strongly suggest not blindly
risking money on your statistical test. Some filtering is required. Look for
trades that make sense.
For example, my software reports that the stocks of MSFT and
GOOG form a meanreverting pair. But I would not trade that spread: too much
idiosyncratic risk. My software also reports that Corn futures and
Soybean Oil futures form a meanreverting pair. But I would not trade that
spread because the economic connection between corn and bean oil is too
weak.
Hope that helps.
Paul
Hi Folks I'm using this to find cointegrated stocks on the
AX. library(xts) library(quantmod) # quickly resource this
file s < function() source('meanrev.R') checkPairFromYahoo <
function(sym1, sym2, dateFilter='::') { t.xts <
getCombined(sym1, sym2, dateFilter=dateFilter) cat("Date range
is", format(start(t.xts)), "to", format(end(t.xts)), "\n") # Build
linear model m < buildLM(t.xts) # Note beta  http://en.wikipedia.org/wiki/Beta_(finance)
beta < getBeta(m) cat("Assumed hedge ratio is", beta,
"\n") # Build spread sprd < buildSpread(t.xts,
beta) # Test cointegration ht <
testCoint(sprd) cat("PP pvalue is", as.double(ht$p.value),
"\n") if (as.double(ht$p.value) < 0.05)
{
cat("###############################################################\n", sym1
,":", sym2 ," is likely meanreverting.\n",
"###########################################################\n" )
} else { #cat(sym1 ,":", sym2 ," is
not meanreverting.\n") } } getCombined < function(sym1,
sym2, dateFilter='::') { # Grab historical data for both
symbols one < getSymbols(sym1, auto.assign=FALSE) two
< getSymbols(sym2, auto.assign=FALSE) # Give columns more
usable names colnames(one) < c('Open', 'High', 'Low', 'Close',
'Volume', 'Adjusted') colnames(two) < c('Open', 'High', 'Low',
'Close', 'Volume', 'Adjusted') # Build combined object
return(merge(one$Close, two$Close, all=FALSE)[dateFilter]) } buildLM
< function(combined) { return(lm(Close ~ Close.1 + 0,
combined)) } getBeta < function(m) {
return(as.double(coef(m)[1])) } buildSpread < function(combined,
beta) { return(combined$Close 
beta*combined$Close.1) } testCoint < function(sprd) {
return(PP.test(sprd, lshort = FALSE)) } I run it on batches of
stockpairs and then have a look at those which are cointegrated. Assuming
my code is right (and anyone who thinks there is something wrong with it please
let me know ;) Just wondered if anyone simply goes with the results, or
if a test of logic is required. I found, for example, that AGL ( a big gas
company) was cointegrated with Bunnings Wharehouses (a hardware superstore
chain). Can't see the reason for that. AMP (major insurer)
cointegrates with AXA (another major insurer). That makes sense and it
cointegrates with Westpac (major bank) still some logic but a bit
thinner. It also cointegrates with Fortescue Metals (big iron ore
operation). Not much logic there. Anyway question is: do you get
better results by using informed judgement on these things or just trust the
figures? Any comments most welcome.
On
19/10/2010 12:35 PM, Yihao Lu aeolus_lu wrote:
I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
Is there anyone who can give me some possible explanation or guide me to some reference? thanks
Best,
Yihao
________________________________
Date: Tue, 19 Oct 2010 09:03:55 +1100
From: [hidden email]
To: [hidden email]
CC: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
Hi
I am still trying to sort this one out. Any comments from anyone would
be most welcome.
Stephen Choularton Ph.D., FIoD
On 14/10/2010 7:29 AM, Stephen Choularton wrote:
Thanks for this help.
Trying to make sense of it so I have added some notes to the code. I
have marked them #?#
Delighted if you can tell me if I am write or wrong, add any comments,
answers.
#?# This appears to be the function that is doing the 'OrnsteinUhlenbeck
#?# process work' particularly via dcOU
#?# I have noted in several places that I am after:
#?# 'the halflife of the decay equals ln(2)/θ'
#?# 'The halflife is given as log(2)/meanreversion speed.'
#?# and I see theta appearing at a number of points in the code.
#?# Can you tell me why 3 thetas viz theta1, theta2, theta3 and what they do?
#?# eg is one of these the theta I am after?
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
#?# random numer generation seed
set.seed(123)
#?# creation of a data set
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
#?# If I Look at X its like this:
#?# Time Series:
#?# Start = 0
#?# End = 1000
#?# Frequency = 1
#?# [1] 1.00000000 etc
#?# What sort of data object is it and how would I coerce an object with one
#?# column from a read.csv into it?
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
#?# This gives:
#?# Maximum likelihood estimation
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# Estimate Std. Error
#?# theta1 3.355322 0.28159504
#?# theta2 1.106107 0.09010627
#?# theta3 2.052815 0.07624441
#?# 2 log L: 3366.389
#?# What's this telling me?
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
#?# This provides me with this output using 'fit' from before:
#?# > vcov(fit)
#?# theta1 theta2 theta3
#?# theta1 0.07929576 0.024620718 0.016634557
#?# theta2 0.02462072 0.008119141 0.005485549
#?# theta3 0.01663456 0.005485549 0.005813209
#?# > confint(fit)
#?# Profiling...
#?# 2.5 % 97.5 %
#?# theta1 2.8448980 3.960982
#?# theta2 0.9433338 1.300629
#?# theta3 1.9147136 2.216113
#?# and 'fit' is:
#?# Call:
#?# mle(minuslogl = OU.lik, start = list(theta1 = 1, theta2 = 0.5,
#?# theta3 = 1), method = "LBFGSB", lower = c(Inf, 0, 0))
#?# Coefficients:
#?# theta1 theta2 theta3
#?# 3.355322 1.106107 2.052815
#?# plus some graphic output
#?# Again, what's this telling me.
#?# This looks like a further example?
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
Please excuse the length of this email (and my lack of understanding)
Hope you can help and thanks.
Stephen Choularton Ph.D., FIoD
On 13/10/2010 2:41 AM, stefano iacus wrote:
just for completeness: OU process is gaussian and transitiion density is known in exact form. So maximum likelihood estimation works fine and I suggest to avoid GMM.
sde package contains exact transition density for this process (e.g. ?dcOU) which you can use to build the likelihood to pass to mle() function.
This example taken from the "inst" directory of the package sde. For the parametrization of the model see ?dcOU
# ex3.01.R
OU.lik < function(theta1, theta2, theta3){
n < length(X)
dt < deltat(X)
sum(dcOU(X[2:n], dt, X[1:(n1)], c(theta1,theta2,theta3), log=TRUE))
}
require(stats4)
require(sde)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit
summary(fit)
# ex3.01.R (cont.)
prof < profile(fit)
par(mfrow=c(1,3))
plot(prof)
par(mfrow=c(1,1))
vcov(fit)
confint(fit)
# ex3.01.R (cont.)
set.seed(123)
X < sde.sim(model="OU", theta=c(3,1,2), N=1000, delta=1e3)
mle(OU.lik, start=list(theta1=1, theta2=0.5, theta3=1),
method="LBFGSB", lower=c(Inf,0,0)) > fit2
summary(fit2)
I hope this helps out
stefano
On 12 Oct 2010, at 12:33, Bjorn Skogtro wrote:
Hi Stephen,
You could take a look at
http://sitmo.com/doc/Calibrating_the_OrnsteinUhlenbeck_model
for the linear regression method, or take a look at the package "sde" which
contains some examples using GMM (not for the OrnsteinUhlenbeck process,
though, only the CIR).
The halflife is given as log(2)/meanreversion speed.
Do keep an eye on the partition of the timeaxis, e.g. what frequency you
are using (daily, yearly) for interpreting the halflife.
BR,
Bjørn

Message: 2
Date: Tue, 12 Oct 2010 05:43:32 0400
From: Sarbo
To: [hidden email]
Subject: Re: [RSIGFinance] OrnsteinUhlenbeck
MessageID:
ContentType: text/plain; charset="utf8"
By halflife, do you mean the speed of meanreversion?
If so, there's a bit of algebraic tomfoolery that's required to
discretise the equation and then fit the data to it. I don't have the
time right now to go into all the details but it's not hard you can
parameterise the process using simple linear regression. If you need
help with that I'll try and get back to you tonight about it.
On Tue, 20101012 at 13:47 +1100, Stephen Choularton wrote:
Hi
Wonder if anyone could point me how I use this method to discover the
half life of a mean reverting process.
I am looking into pair trading and the time it takes for a
cointegrated pair to revert to the norm.

Stephen Choularton Ph.D., FIoD
9999 2226
0413 545 182
for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions
should go.
 next part 
An HTML attachment was scrubbed...
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.html
 next part 
A nontext attachment was scrubbed...
Name: CoS2010Winner.JPG
Type: image/jpeg
Size: 16091 bytes
Desc: not available
URL: <
https://stat.ethz.ch/pipermail/rsigfinance/attachments/20101012/26e32fc7/attachment0001.jpe

_______________________________________________
RSIGFinance mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/rsigfinance
End of RSIGFinance Digest, Vol 77, Issue 8
********************************************
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.

Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I20123 Milan  Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus

Please don't send me Word or PowerPoint attachments if not
absolutely necessary. See:
http://www.gnu.org/philosophy/nowordattachments.html
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance 
Subscriberposting only. If you want to post, subscribe first.  Also
note that this is not the rhelp list where general R questions should
go.
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance
 Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.
No virus found in this incoming message.
Checked by AVG  www.avg.com
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


Thank you and thank Prof. Zivot
Best,
Yihao
From: [hidden email]
To: [hidden email]
Date: Tue, 19 Oct 2010 06:59:37 0400
Subject: Re: [RSIGFinance] Mean reversion
Yihao,
Prof. Zivot is right. The ADF test isn't a great way to test for
meanreversion; it's merely a way to test for stationarity to specify
the degrees in an ARIMA model.
I dug up some code from my misspent youth as a consultant which you
might find useful:
StochasticProcessTest < function(PriceSeries, delta.t, p.value,
diagnostics = TRUE, from = NULL, to = NULL,
by = NULL, currency = '($)'){
require(stats)
require(fSeries)
m < length(PriceSeries)
S1 < PriceSeries[1:(m1)]
S2 < PriceSeries[2:m]
#Fit a GBM process:
Y < diff(log(PriceSeries)); X < S1
GBMfit < lm(Y ~ X)
#Fit a meanreverting GBM process:
Y < diff(PriceSeries) / S1; X < log(S1)
MRGBMfit < lm(Y ~ X)
#Fit a Vasicek (OU) process:
Y < diff(PriceSeries); X < S1
Vfit < lm(Y ~ X)
#Fit a CoxIngersollRoss process:
Y < diff(PriceSeries) / sqrt(S1); X < S1 / sqrt(S1)
CIRfit < lm(Y ~ X)
#Gather the parameter estimates:
kappa < as.vector((c(0, MRGBMfit$coef[2], Vfit$coef[2], CIRfit
$coef[2])) / delta.t)
mu < as.vector((c(mean(log(S2/S1)), MRGBMfit$coef[1] / kappa[2], Vfit
$coef[1] / kappa[3],
CIRfit$coef[1] / kappa[4])) / delta.t)
sigma < (c(sd(GBMfit$resid), sd(MRGBMfit$resid), sd(Vfit$resid),
sd(CIRfit$resid))) / sqrt(delta.t)
tstat < as.vector(c(summary(GBMfit)$coef[2,3],
summary(MRGBMfit)$coef[2,3], summary(Vfit)$coef[2,3],
summary(CIRfit)$coef[2,3]))
fstat < list(summary(GBMfit)$fstatistic,
summary(MRGBMfit)$fstatistic, summary(Vfit)$fstatistic,
summary(CIRfit)$fstatistic)
names(fstat) < c('GBM', 'Mean.Revert.GBM', 'Vasicek', 'CIR')
AICs < c(AIC(GBMfit), AIC(MRGBMfit), AIC(Vfit), AIC(CIRfit))
paramframe < data.frame(rbind(kappa, mu, sigma, tstat, AICs))
names(paramframe) < names(fstat)
#Now figure out what the actual process is, using AIC:
crit < ifelse(m > 30, qnorm(1  p.value), qt(1  p.value, df = n))
tmp < which.min(AICs)
Processes < names(fstat)
Verdict < Processes[tmp]
FinalSummary < switch(Verdict, GBM = summary(GBMfit), CIR =
summary(CIRfit), Mean.Revert.GBM = MRGBMfit,
Vasicek = Vfit)
fitobj < switch(Verdict, GBM = GBMfit, CIR = CIRfit, Mean.Revert.GBM
= MRGBMfit, Vasicek = Vfit)
Output < list(Parameters = paramframe, Critical.Value = crit, Verdict
= Verdict, FinalSummary = FinalSummary,
fstat = fstat, fitted.object = fitobj)
if (diagnostics){
op < par(ask = TRUE)
on.exit(op)
if(!all(c(class(from), class(to)) == 'Date')){
S < timeSeries(PriceSeries)
} else S = timeSeries(PriceSeries, seq(from, to, length.out = m))
plot(S, type = 'l', xlab = 'Date', ylab = paste('Price Series',
currency), main = 'Time Series Plot of Data',
lwd = 2, col = 'blue')
rets < returns(PriceSeries, 'continuous')[1]
hist(rets, xlab = paste('LogReturns', currency), col = 'blue',
border = 'white', main = 'Histogram of Return Series',
freq = FALSE)
x < seq(min(rets), max(rets), length.out = max(m, 1000))
lines(x, dnorm(x, mean(rets), sd(rets)), col = 'magenta', lwd = 2)
lines(density(rets), col = 'green', lwd = 2)
legend('topright', legend = c('LogReturns', 'Observed CDF',
'Gaussian Fit'), lwd = rep(2, 3),
col = c('blue', 'green', 'magenta'))
plot(fitobj, 1:6)
}
return(Output)
}
(I don't claim that it's necessarily great code, but it does seem to
work.)
On Mon, 20101018 at 21:35 0400, Yihao Lu aeolus_lu wrote:
> I am doing rolling ADF test on some time series to check mean reversion. When I use short period rolling, I find the residue is not stationary at all. However, when I use horizon longer than 5 years, I find very significant stationary. On the other hand, I find the half life is only around 30 days.
> Is there anyone who can give me some possible explanation or guide me to some reference? thanks
>
> Best,
> Yihao
[[alternative HTML version deleted]]
_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/rsigfinance Subscriberposting only. If you want to post, subscribe first.
 Also note that this is not the rhelp list where general R questions should go.


This post has NOT been accepted by the mailing list yet.
Hi Paul,
I am very much impressed the way you explain your things. I have on question with regard to Mean Reversion I got various pairs my idea is to identify the indictor which will give me an indication of reversion. Can you highlight any method which would probably help me to identify such reversion.
Thanks

