GARCH Estimation Problem---- This is not a R problem but an econometric problem

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GARCH Estimation Problem---- This is not a R problem but an econometric problem

KAUSHIK BHATTACHARJEE
 
Hi All,
I need your help.
I have 9 stock returns(y) to analyze. I am running an regression : y on lagged values of Y and X1&X2 (exogenous variables). If I run an ols  regression then  LM test etc on the residuals shows existence of GARCH  effect.(although there are serial correlation present in the residuals  too but they are mild i.e. significant at 10% level )
Therefore I proceed to model the volatility using an appropriate GARCH model. Going by the method suggested by Walter Enders calculate RSS’, AIC’ , BIC’ etc. I restricted my search in 6 models ....from  GARCH(1,1) to GARCH(2,2) only. Suppose these exercises is suggesting  me a GARCH(1,1) or EGARCH(1,1) model. But after I fit the model and collect the residuals and subject  them  to tests, I observe: though there are no GARCH effect left (LB stat is giving p-values as 0.9999 for squared residuals ) but I am finding serial correlations of the residuals have increased(now almost all of them are significant at 5% level).So it appears GARCH modeling is taking care of GARCH effect but spuriously introducing serial correlation in the residuals.
I have checked with model specifications ..theoretically it seems ok and this phenomena is true for 3 stocks out of 9. Rest 6 are yielding  nice/good results in terms no serial correlation in both residuals and squared residuals.
So where the estimation/ GARCH modeling is going wrong? Why this is happening.Anyidea?
Also if the sum of the coefficients (constant+ ARCH term + GARCH Term) is greater than one(1) then what does this imply? Should I Go for an I-GARCH model even if my dependent variable in the mean equation is I(0).
 Kaushik Bhattacharjee



     
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Re: GARCH Estimation Problem---- This is not a Rproblem but an econometric problem

Adams, Zeno
I do not know if the GARCH part actually "introduces" serial correlation but it suggests that your dynamic structure is not complete and that you should add more (possibly higher order) autoregressive terms into the mean equation. This should solve autocorrelation problem.
If (ARCH term + GARCH Term) is larger than one then the variance is not stationary. In this case you should restrict (ARCH term + GARCH Term) to sum to one (using the I_GARCH model). Otherwise your parameters violate an important assumption of the GARCH model (e.g. the long-run variance  constant/(1- (ARCH term + GARCH Term)) would become negative.

Zeno

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of KAUSHIK BHATTACHARJEE
Sent: Montag, 14. Juni 2010 10:51
To: R Finance
Subject: [R-SIG-Finance] GARCH Estimation Problem---- This is not a Rproblem but an econometric problem

Â
Hi All,
I need your help.
I have 9 stock returns(y) to analyze. I am running an regression : y on lagged values of Y and X1&X2 (exogenous variables). If I run an ols  regression then  LM test etc on the residuals shows existence of GARCH  effect.(although there are serial correlation present in the residuals  too but they are mild i.e. significant at 10% level ) Therefore I proceed to model the volatility using an appropriate GARCH model. Going by the method suggested by Walter Enders calculate RSS’, AIC’ , BIC’ etc. I restricted my search in 6 models ....from  GARCH(1,1) to GARCH(2,2) only. Suppose these exercises is suggesting  me a GARCH(1,1) or EGARCH(1,1) model. But after I fit the model and collect the residuals and subject  them  to tests, I observe: though there are no GARCH effect left (LB stat is giving p-values as 0.9999 for squared residuals ) but I am finding serial correlations of the residuals have increased(now almost all of them are significant at 5% level).So it appears GARCH modeling is taking care of GARCH effect but spuriously introducing serial correlation in the residuals.
I have checked with model specifications ..theoretically it seems ok and this phenomena is true for 3 stocks out of 9. Rest 6 are yielding  nice/good results in terms no serial correlation in both residuals and squared residuals.
So where the estimation/ GARCH modeling is going wrong? Why this is happening.Anyidea?
Also if the sum of the coefficients (constant+ ARCH term + GARCH Term) is greater than one(1) then what does this imply? Should I Go for an I-GARCH model even if my dependent variable in the mean equation is I(0).
 Kaushik Bhattacharjee



     
        [[alternative HTML version deleted]]


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Re: GARCH Estimation Problem---- This is not a R problem but an econometric problem

Patrick Burns-2
In reply to this post by KAUSHIK BHATTACHARJEE
I don't know what is going on, but I'm
suspecting that LB p-value = .9999 is a
hint.

That p-value of essentially 1 is trying to
say that the squared residuals are systematically
anti autocorrelated.  That's unlikely to be
true.  More likely is that one or more outliers
are skewing the test -- the Burns Statistics
working paper on Ljung-Box talks about this and
says what test to use.

My guess is that the outlier(s) are not only
affecting the Ljung-Box test but estimation as
well.  Assuming a t-distribution rather than a
Gaussian in the garch estimate might help, but
perhaps Winsorizing the returns would be a more
profitable route.

Reality seems to be a more interesting story than
can be told with the simple model used so far.

On 14/06/2010 09:50, KAUSHIK BHATTACHARJEE wrote:

> Â
> Hi All,
> I need your help.
> I have 9 stock returns(y) to analyze. I am running an regression : y on lagged values of Y and X1&X2 (exogenous variables). If I run an ols  regression then  LM test etc on the residuals shows existence of GARCH  effect.(although there are serial correlation present in the residuals  too but they are mild i.e. significant at 10% level )
> Therefore I proceed to model the volatility using an appropriate GARCH model. Going by the method suggested by Walter Enders calculate RSS’, AIC’ , BIC’ etc. I restricted my search in 6 models ....from  GARCH(1,1) to GARCH(2,2) only. Suppose these exercises is suggesting  me a GARCH(1,1) or EGARCH(1,1) model. But after I fit the model and collect the residuals and subject  them  to tests, I observe: though there are no GARCH effect left (LB stat is giving p-values as 0.9999 for squared residuals ) but I am finding serial correlations of the residuals have increased(now almost all of them are significant at 5% level).So it appears GARCH modeling is taking care of GARCH effect but spuriously introducing serial correlation in the residuals.
> I have checked with model specifications ..theoretically it seems ok and this phenomena is true for 3 stocks out of 9. Rest 6 are yielding  nice/good results in terms no serial correlation in both residuals and squared residuals.
> So where the estimation/ GARCH modeling is going wrong? Why this is happening.Anyidea?
> Also if the sum of the coefficients (constant+ ARCH term + GARCH Term) is greater than one(1) then what does this imply? Should I Go for an I-GARCH model even if my dependent variable in the mean equation is I(0).
> Â Kaushik Bhattacharjee
>
>
>
>
> [[alternative HTML version deleted]]
>
>
>
>
> _______________________________________________
> [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.

--
Patrick Burns
[hidden email]
http://www.burns-stat.com

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