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

Mon Jun 14 12:46:37 CEST 2010

```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: r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] 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 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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