Rugarch for EWMA/VaR

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Rugarch for EWMA/VaR

ThomasF
Dear R-Users, dear Alexios,

I am trying to use rugarch to forecast volatiliy and do VaR-backtests using the Exponentially weighted moving average.
To achieve this I used the iGarch, set omega to 0 and either estimate or fix alpha1 and beta1. Example code is provided at the end of my post.

Some issues came up which I'd be glad to solve with your help:

1) Whenever i try to fit alpha1 and beta1, I always get 0.5 as result. I tried this for different underlyings and time horizons. Any idea what the reason could be?

2) I also get an error (I translated the error message to english) after the  ARCH LM Test output:

ARCH LM Tests
------------------------------------
             Statistic DoF P-Value
ARCH Lag[2]      4.653   2 0.09765
ARCH Lag[5]      7.991   5 0.15672
ARCH Lag[10]    12.082  10 0.27959
Error in names(ans) = c("10%", "5%", "1%") :
  Attribut 'names' [3] must have same length as the vector [0]

Is there something wrong with my code or the way i put the data into the model? The other part of the outputs seems legit.

3) when I tried to do the same calculations with fixed alpha i get the following error when i try to filter the model:

1: In doTryCatch(return(expr), name, parentenv, handler) :
  passing an object of type 'NULL' to .C (arg 8) is deprecated
2: In doTryCatch(return(expr), name, parentenv, handler) :
  passing an object of type 'NULL' to .C (arg 9) is deprecated

The ugarchfilter output seems reasonable again.

4)  I am not able to generate a rolling forecast and VaR Output when i fixed alpha1. Could you please give me a hint on how to do this with filtered data?

5) Does any of those issues arise of the use of the data as "zoo" object?


Thanks in advance for your effort to help me

Sincerely

Thomas


-----------------Code----------


################
###Download Data & Compute Returns
################

library ("tseries")

#adjusted close price of sp500
sp500price=get.hist.quote(instrument="^gspc", start="2006-01-01", end="2011-12-31", quote="AdjClose")

# returns
sp500returns=diff(log(sp500price))


library("rugarch")



##############
### Use iGarch for EWMA - fitted alpha and beta
##############


### Model spec
spec1= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1, 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE), distribution.model = "norm", fixed.pars = list(omega=0))

###Fit Model
fit1= ugarchfit(spec=spec1, data=sp500returns, out.sample=0, solver="solnp", solver.control=list(trace=0))
show(fit1)

#### rolling forecast und VaR
roll1=ugarchroll(spec=spec1, data=sp500returns, n.ahead=1, forecast.length=500, refit.every=25, refit.window="recursive", solver="solnp", solver.control=list(tol=1e-05, delta=1e-06, trace=0), calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))

report(roll1, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
report(roll1, type="fpm")
plot(roll1, which="all")




##############
### Use iGarch for EWMA - fixed alpha and beta with lambda=0.94
##############


### Model spec
spec2= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1, 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE), distribution.model = "norm",  fixed.pars = list(omega=0, alpha1=0.06))

###Fit Model???

fit2= ugarchfit(spec=spec2, data=sp500returns, out.sample=0, solver="solnp", solver.control=list(trace=0))
show(fit2)

### filter model
filt2= ugarchfilter(spec=spec2, data=sp500returns)
show(filt2)

#### rolling forecast und VaR

roll2=ugarchroll(spec=spec2, data=sp500returns, n.ahead=1, forecast.length=500,   calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))

report(roll2, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)

report(roll2, type="fpm")
plot(roll2, which="all")
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Re: Rugarch for EWMA/VaR

alexios
Thomas,

1. The problem with the iGARCH model (related to a bad default setting)
was fixed some time ago in the r-forge version (will be available on
CRAN when I next update it there...since it is frowned upon to update a
CRAN package more than 12 times in a year, you should look to r-forge
for the 'newest' version at any time).
You have 2 options:
1. Download the latest version from r-forge OR,
2. In ugarchfit set the option "fit.control=list(stationarity=FALSE)"

2. That's definitely a problem in the summary method. Will investigate
when I get a moment.

3. The error with the ugarchfilter C function, related to the newest
version of R, was also fixed in the r-forge release.

4. You can't roll when all the parameters are fixed. It does not even
make sense! Roll implies that you are fitting, forecasting, re-fitting.
Since you have all parameters fixed then just use the filter method on
the data you want to forecast 1-ahead, else use the forecast method with
a spec object and out of sample specified.

-Alexios

On 03/05/2012 21:23, ThomasF wrote:

> Dear R-Users, dear Alexios,
>
> I am trying to use rugarch to forecast volatiliy and do VaR-backtests using
> the Exponentially weighted moving average.
> To achieve this I used the iGarch, set omega to 0 and either estimate or fix
> alpha1 and beta1. Example code is provided at the end of my post.
>
> Some issues came up which I'd be glad to solve with your help:
>
> 1) Whenever i try to fit alpha1 and beta1, I always get 0.5 as result. I
> tried this for different underlyings and time horizons. Any idea what the
> reason could be?
>
> 2) I also get an error (I translated the error message to english) after the
> ARCH LM Test output:
>
> ARCH LM Tests
> ------------------------------------
>               Statistic DoF P-Value
> ARCH Lag[2]      4.653   2 0.09765
> ARCH Lag[5]      7.991   5 0.15672
> ARCH Lag[10]    12.082  10 0.27959
> Error in names(ans) = c("10%", "5%", "1%") :
>    Attribut 'names' [3] must have same length as the vector [0]
>
> Is there something wrong with my code or the way i put the data into the
> model? The other part of the outputs seems legit.
>
> 3) when I tried to do the same calculations with fixed alpha i get the
> following error when i try to filter the model:
>
> 1: In doTryCatch(return(expr), name, parentenv, handler) :
>    passing an object of type 'NULL' to .C (arg 8) is deprecated
> 2: In doTryCatch(return(expr), name, parentenv, handler) :
>    passing an object of type 'NULL' to .C (arg 9) is deprecated
>
> The ugarchfilter output seems reasonable again.
>
> 4)  I am not able to generate a rolling forecast and VaR Output when i fixed
> alpha1. Could you please give me a hint on how to do this with filtered
> data?
>
> 5) Does any of those issues arise of the use of the data as "zoo" object?
>
>
> Thanks in advance for your effort to help me
>
> Sincerely
>
> Thomas
>
>
> -----------------Code----------
>
>
> ################
> ###Download Data&  Compute Returns
> ################
>
> library ("tseries")
>
> #adjusted close price of sp500
> sp500price=get.hist.quote(instrument="^gspc", start="2006-01-01",
> end="2011-12-31", quote="AdjClose")
>
> # returns
> sp500returns=diff(log(sp500price))
>
>
> library("rugarch")
>
>
>
> ##############
> ### Use iGarch for EWMA - fitted alpha and beta
> ##############
>
>
> ### Model spec
> spec1= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1,
> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
> distribution.model = "norm", fixed.pars = list(omega=0))
>
> ###Fit Model
> fit1= ugarchfit(spec=spec1, data=sp500returns, out.sample=0, solver="solnp",
> solver.control=list(trace=0))
> show(fit1)
>
> #### rolling forecast und VaR
> roll1=ugarchroll(spec=spec1, data=sp500returns, n.ahead=1,
> forecast.length=500, refit.every=25, refit.window="recursive",
> solver="solnp", solver.control=list(tol=1e-05, delta=1e-06, trace=0),
> calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>
> report(roll1, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
> report(roll1, type="fpm")
> plot(roll1, which="all")
>
>
>
>
> ##############
> ### Use iGarch for EWMA - fixed alpha and beta with lambda=0.94
> ##############
>
>
> ### Model spec
> spec2= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1,
> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
> distribution.model = "norm",  fixed.pars = list(omega=0, alpha1=0.06))
>
> ###Fit Model???
>
> fit2= ugarchfit(spec=spec2, data=sp500returns, out.sample=0, solver="solnp",
> solver.control=list(trace=0))
> show(fit2)
>
> ### filter model
> filt2= ugarchfilter(spec=spec2, data=sp500returns)
> show(filt2)
>
> #### rolling forecast und VaR
>
> roll2=ugarchroll(spec=spec2, data=sp500returns, n.ahead=1,
> forecast.length=500,   calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>
> report(roll2, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
>
> report(roll2, type="fpm")
> plot(roll2, which="all")
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Rugarch-for-EWMA-VaR-tp4607011.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

_______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.
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Re: Rugarch for EWMA/VaR

ThomasF
 Hello Alexios,

thank you for your quick reply.

I'm going to download the newest version from R-Forge.

Concerning 4) I still have problems.
I tried something like:
forc2=ugarchforecast(spec=spec2, data=sp500returns, n.ahead=1, out.sample=500, calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))  
and
forc2=ugarchforecast(spec=spec2, data=sp500returns, n.ahead=1, out.sample=500)
what didn't work for me.

I would like to be able to generate VaR-Backtesting Results and VaR-exceedence-graphs like I did with the fitted model.
Could you please help me out, maybe with some lines of code? I already checked the example codes I could find on how to combine forecasting with fixed parameters and getting the VaR-Output and still didn't manage to do it.

Thomas




alexios wrote
Thomas,

1. The problem with the iGARCH model (related to a bad default setting)
was fixed some time ago in the r-forge version (will be available on
CRAN when I next update it there...since it is frowned upon to update a
CRAN package more than 12 times in a year, you should look to r-forge
for the 'newest' version at any time).
You have 2 options:
1. Download the latest version from r-forge OR,
2. In ugarchfit set the option "fit.control=list(stationarity=FALSE)"

2. That's definitely a problem in the summary method. Will investigate
when I get a moment.

3. The error with the ugarchfilter C function, related to the newest
version of R, was also fixed in the r-forge release.

4. You can't roll when all the parameters are fixed. It does not even
make sense! Roll implies that you are fitting, forecasting, re-fitting.
Since you have all parameters fixed then just use the filter method on
the data you want to forecast 1-ahead, else use the forecast method with
a spec object and out of sample specified.

-Alexios

On 03/05/2012 21:23, ThomasF wrote:
> Dear R-Users, dear Alexios,
>
> I am trying to use rugarch to forecast volatiliy and do VaR-backtests using
> the Exponentially weighted moving average.
> To achieve this I used the iGarch, set omega to 0 and either estimate or fix
> alpha1 and beta1. Example code is provided at the end of my post.
>
> Some issues came up which I'd be glad to solve with your help:
>
> 1) Whenever i try to fit alpha1 and beta1, I always get 0.5 as result. I
> tried this for different underlyings and time horizons. Any idea what the
> reason could be?
>
> 2) I also get an error (I translated the error message to english) after the
> ARCH LM Test output:
>
> ARCH LM Tests
> ------------------------------------
>               Statistic DoF P-Value
> ARCH Lag[2]      4.653   2 0.09765
> ARCH Lag[5]      7.991   5 0.15672
> ARCH Lag[10]    12.082  10 0.27959
> Error in names(ans) = c("10%", "5%", "1%") :
>    Attribut 'names' [3] must have same length as the vector [0]
>
> Is there something wrong with my code or the way i put the data into the
> model? The other part of the outputs seems legit.
>
> 3) when I tried to do the same calculations with fixed alpha i get the
> following error when i try to filter the model:
>
> 1: In doTryCatch(return(expr), name, parentenv, handler) :
>    passing an object of type 'NULL' to .C (arg 8) is deprecated
> 2: In doTryCatch(return(expr), name, parentenv, handler) :
>    passing an object of type 'NULL' to .C (arg 9) is deprecated
>
> The ugarchfilter output seems reasonable again.
>
> 4)  I am not able to generate a rolling forecast and VaR Output when i fixed
> alpha1. Could you please give me a hint on how to do this with filtered
> data?
>
> 5) Does any of those issues arise of the use of the data as "zoo" object?
>
>
> Thanks in advance for your effort to help me
>
> Sincerely
>
> Thomas
>
>
> -----------------Code----------
>
>
> ################
> ###Download Data&  Compute Returns
> ################
>
> library ("tseries")
>
> #adjusted close price of sp500
> sp500price=get.hist.quote(instrument="^gspc", start="2006-01-01",
> end="2011-12-31", quote="AdjClose")
>
> # returns
> sp500returns=diff(log(sp500price))
>
>
> library("rugarch")
>
>
>
> ##############
> ### Use iGarch for EWMA - fitted alpha and beta
> ##############
>
>
> ### Model spec
> spec1= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1,
> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
> distribution.model = "norm", fixed.pars = list(omega=0))
>
> ###Fit Model
> fit1= ugarchfit(spec=spec1, data=sp500returns, out.sample=0, solver="solnp",
> solver.control=list(trace=0))
> show(fit1)
>
> #### rolling forecast und VaR
> roll1=ugarchroll(spec=spec1, data=sp500returns, n.ahead=1,
> forecast.length=500, refit.every=25, refit.window="recursive",
> solver="solnp", solver.control=list(tol=1e-05, delta=1e-06, trace=0),
> calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>
> report(roll1, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
> report(roll1, type="fpm")
> plot(roll1, which="all")
>
>
>
>
> ##############
> ### Use iGarch for EWMA - fixed alpha and beta with lambda=0.94
> ##############
>
>
> ### Model spec
> spec2= ugarchspec (variance.model = list(model = "iGARCH", garchOrder = c(1,
> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
> distribution.model = "norm",  fixed.pars = list(omega=0, alpha1=0.06))
>
> ###Fit Model???
>
> fit2= ugarchfit(spec=spec2, data=sp500returns, out.sample=0, solver="solnp",
> solver.control=list(trace=0))
> show(fit2)
>
> ### filter model
> filt2= ugarchfilter(spec=spec2, data=sp500returns)
> show(filt2)
>
> #### rolling forecast und VaR
>
> roll2=ugarchroll(spec=spec2, data=sp500returns, n.ahead=1,
> forecast.length=500,   calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>
> report(roll2, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
>
> report(roll2, type="fpm")
> plot(roll2, which="all")
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Rugarch-for-EWMA-VaR-tp4607011.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

_______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.
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Re: Rugarch for EWMA/VaR

alexios
Thomas,

You need to read the documentation more carefully (you forgot to declare
the n.roll option).

Example:
library(rugarch)
data(sp500ret)

spec= ugarchspec (variance.model = list(model = "iGARCH", garchOrder =
c(1,1)), mean.model=list(armaOrder=c(0,0),include.mean=TRUE),
distribution.model = "norm",  fixed.pars = list(mu =
mean(sp500ret[1:100,1]),omega=0, alpha1=0.06))

# forecast the model starting from t=101 to 1=1500
# forecast = 1-ahead x 1399 rolls = 1400 forecasts (includes the first #
forecast as the 'zero' roll)

forecast = ugarchforecast(spec, sp500ret[1:1500,,drop=FALSE], n.roll =
1399, n.ahead = 1, out.sample=1400)

# conditional mean (just a constant)
cmu = as.numeric(as.data.frame(forecast, which = "series",
rollframe="all", aligned = FALSE))
# conditional sigma
csigma = as.numeric(as.data.frame(forecast, which = "sigma",
rollframe="all", aligned = FALSE))

# use location+scaling transformation property of normal distribution:
VaR1 = qnorm(0.01)*csigma + cmu
VaR5 = qnorm(0.05)*csigma + cmu

dates = as.Date(rownames(sp500ret)[101:1500])
plot(dates, sp500ret[101:1500,1])
lines(dates, VaR1, col = "blue")
lines(dates, VaR5, col = "brown")

# VaR Exceedances Test
VaRTest(alpha = 0.01, actual = sp500ret[101:1500,1], VaR = VaR1)
VaRTest(alpha = 0.05, actual = sp500ret[101:1500,1], VaR = VaR5)

# VaR Duration Test
VaRDurTest(alpha = 0.01, actual = sp500ret[101:1500,1], VaR = VaR1)
VaRDurTest(alpha = 0.05, actual = sp500ret[101:1500,1], VaR = VaR5)



-Alexios


On 03/05/2012 23:05, ThomasF wrote:

>   Hello Alexios,
>
> thank you for your quick reply.
>
> I'm going to download the newest version from R-Forge.
>
> Concerning 4) I still have problems.
> I tried something like:
> forc2=ugarchforecast(spec=spec2, data=sp500returns, n.ahead=1,
> out.sample=500, calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
> and
> forc2=ugarchforecast(spec=spec2, data=sp500returns, n.ahead=1,
> out.sample=500)
> what didn't work for me.
>
> I would like to be able to generate VaR-Backtesting Results and
> VaR-exceedence-graphs like I did with the fitted model.
> Could you please help me out, maybe with some lines of code? I already
> checked the example codes I could find on how to combine forecasting with
> fixed parameters and getting the VaR-Output and still didn't manage to do
> it.
>
> Thomas
>
>
>
>
>
> alexios wrote
>>
>> Thomas,
>>
>> 1. The problem with the iGARCH model (related to a bad default setting)
>> was fixed some time ago in the r-forge version (will be available on
>> CRAN when I next update it there...since it is frowned upon to update a
>> CRAN package more than 12 times in a year, you should look to r-forge
>> for the 'newest' version at any time).
>> You have 2 options:
>> 1. Download the latest version from r-forge OR,
>> 2. In ugarchfit set the option "fit.control=list(stationarity=FALSE)"
>>
>> 2. That's definitely a problem in the summary method. Will investigate
>> when I get a moment.
>>
>> 3. The error with the ugarchfilter C function, related to the newest
>> version of R, was also fixed in the r-forge release.
>>
>> 4. You can't roll when all the parameters are fixed. It does not even
>> make sense! Roll implies that you are fitting, forecasting, re-fitting.
>> Since you have all parameters fixed then just use the filter method on
>> the data you want to forecast 1-ahead, else use the forecast method with
>> a spec object and out of sample specified.
>>
>> -Alexios
>>
>> On 03/05/2012 21:23, ThomasF wrote:
>>> Dear R-Users, dear Alexios,
>>>
>>> I am trying to use rugarch to forecast volatiliy and do VaR-backtests
>>> using
>>> the Exponentially weighted moving average.
>>> To achieve this I used the iGarch, set omega to 0 and either estimate or
>>> fix
>>> alpha1 and beta1. Example code is provided at the end of my post.
>>>
>>> Some issues came up which I'd be glad to solve with your help:
>>>
>>> 1) Whenever i try to fit alpha1 and beta1, I always get 0.5 as result. I
>>> tried this for different underlyings and time horizons. Any idea what the
>>> reason could be?
>>>
>>> 2) I also get an error (I translated the error message to english) after
>>> the
>>> ARCH LM Test output:
>>>
>>> ARCH LM Tests
>>> ------------------------------------
>>>                Statistic DoF P-Value
>>> ARCH Lag[2]      4.653   2 0.09765
>>> ARCH Lag[5]      7.991   5 0.15672
>>> ARCH Lag[10]    12.082  10 0.27959
>>> Error in names(ans) = c("10%", "5%", "1%") :
>>>     Attribut 'names' [3] must have same length as the vector [0]
>>>
>>> Is there something wrong with my code or the way i put the data into the
>>> model? The other part of the outputs seems legit.
>>>
>>> 3) when I tried to do the same calculations with fixed alpha i get the
>>> following error when i try to filter the model:
>>>
>>> 1: In doTryCatch(return(expr), name, parentenv, handler) :
>>>     passing an object of type 'NULL' to .C (arg 8) is deprecated
>>> 2: In doTryCatch(return(expr), name, parentenv, handler) :
>>>     passing an object of type 'NULL' to .C (arg 9) is deprecated
>>>
>>> The ugarchfilter output seems reasonable again.
>>>
>>> 4)  I am not able to generate a rolling forecast and VaR Output when i
>>> fixed
>>> alpha1. Could you please give me a hint on how to do this with filtered
>>> data?
>>>
>>> 5) Does any of those issues arise of the use of the data as "zoo" object?
>>>
>>>
>>> Thanks in advance for your effort to help me
>>>
>>> Sincerely
>>>
>>> Thomas
>>>
>>>
>>> -----------------Code----------
>>>
>>>
>>> ################
>>> ###Download Data&   Compute Returns
>>> ################
>>>
>>> library ("tseries")
>>>
>>> #adjusted close price of sp500
>>> sp500price=get.hist.quote(instrument="^gspc", start="2006-01-01",
>>> end="2011-12-31", quote="AdjClose")
>>>
>>> # returns
>>> sp500returns=diff(log(sp500price))
>>>
>>>
>>> library("rugarch")
>>>
>>>
>>>
>>> ##############
>>> ### Use iGarch for EWMA - fitted alpha and beta
>>> ##############
>>>
>>>
>>> ### Model spec
>>> spec1= ugarchspec (variance.model = list(model = "iGARCH", garchOrder =
>>> c(1,
>>> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
>>> distribution.model = "norm", fixed.pars = list(omega=0))
>>>
>>> ###Fit Model
>>> fit1= ugarchfit(spec=spec1, data=sp500returns, out.sample=0,
>>> solver="solnp",
>>> solver.control=list(trace=0))
>>> show(fit1)
>>>
>>> #### rolling forecast und VaR
>>> roll1=ugarchroll(spec=spec1, data=sp500returns, n.ahead=1,
>>> forecast.length=500, refit.every=25, refit.window="recursive",
>>> solver="solnp", solver.control=list(tol=1e-05, delta=1e-06, trace=0),
>>> calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>>>
>>> report(roll1, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
>>> report(roll1, type="fpm")
>>> plot(roll1, which="all")
>>>
>>>
>>>
>>>
>>> ##############
>>> ### Use iGarch for EWMA - fixed alpha and beta with lambda=0.94
>>> ##############
>>>
>>>
>>> ### Model spec
>>> spec2= ugarchspec (variance.model = list(model = "iGARCH", garchOrder =
>>> c(1,
>>> 1)), mean.model=list(armaOrder=c(0,0),include.mean=FALSE),
>>> distribution.model = "norm",  fixed.pars = list(omega=0, alpha1=0.06))
>>>
>>> ###Fit Model???
>>>
>>> fit2= ugarchfit(spec=spec2, data=sp500returns, out.sample=0,
>>> solver="solnp",
>>> solver.control=list(trace=0))
>>> show(fit2)
>>>
>>> ### filter model
>>> filt2= ugarchfilter(spec=spec2, data=sp500returns)
>>> show(filt2)
>>>
>>> #### rolling forecast und VaR
>>>
>>> roll2=ugarchroll(spec=spec2, data=sp500returns, n.ahead=1,
>>> forecast.length=500,   calculate.VaR=TRUE, VaR.alpha=c(0.01, 0.05))
>>>
>>> report(roll2, type="VaR", n.ahead=1, VaR.alpha=0.01, conf.level=0.95)
>>>
>>> report(roll2, type="fpm")
>>> plot(roll2, which="all")
>>>
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