# [R-SIG-Finance] GARCH Estimation Problem---- This is not a R problem but an econometric problem

Patrick Burns patrick at burns-stat.com
Mon Jun 14 13:01:54 CEST 2010

```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
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 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 olsÂ  regression thenÂ  LM test etc on the residuals shows existence of GARCHÂ  effect.(although there are serial correlation present in the residuals Â 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 RSSâ€™, AICâ€™ , BICâ€™ etc. I restricted my search in 6 models ....fromÂ  GARCH(1,1) to GARCH(2,2) only. Suppose these exercises is suggestingÂ  me a GARCH(1,1) or EGARCH(1,1) model. But after I fit the model and collect the residuals and subject Â them Â 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 yieldingÂ  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
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--
Patrick Burns
patrick at burns-stat.com
http://www.burns-stat.com

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