I am currently writing my thesis about GARCH modeling of a financial return series. More specifically, I first modelled the return $r_t$ within the following equation: $r_t = \epsilon_t$. In other words, I dropped any mean equation (e.g. ARMA) and tried to model the return series solely as a GARCH(1,1). I made all the pretests (ARCH-LM, ..), there are GARCH effects. My estimation also produced highly significant results (see first picture). enter image description here

However, when predicting the residuals via "predict myresiduals, residuals" and testing them in terms of no more GARCH effects, then tests for autocorrelation etc. all indicate that there still are GARCH effects (i.e. volatility clustering). I then thought maybe I should add an ARMA(1,1) mean equation. I did and I, again, got significant results for both ARMA and GARCH parameters (see picture 2). enter image description here

But again, when predicting the residuals and testing whether the volatility clustering was taken care of, there is still volatility clustering in the residuals. What do I do wrong?


1 Answer 1


Do you by any chance "predict" raw residuals rather than standardized residuals? (Then you would get exactly the same result of the ARCH-LM test when "pre-testing" and when "post-testing" in the case of no conditional mean model $r_t=\epsilon_t$.) The raw residuals will contain ARCH effects and that is why you want to apply a GARCH model and obtain standardized residuals that do not contain ARCH effects.

On the other hand, if you find ARCH effects in the standardized residuals, the GARCH model you are using may be inappropriate. Try different variants of the GARCH model (EGARCH, APARCH and whatever else) and different lag orders.

Also note that the original ARCH-LM test is inappropriate for testing for remaining ARCH effects in the standardized residuals of a GARCH model; Li-Mak test should be used instead. (I do not know whether the Li-Mak test is available in Stata. Also, use of the original ARCH-LM test seems to be relatively widespread in the applied literature, even though it is inappropriate.)


  • Li, W. K. and Mak, T. K. (1994) On the squared residual autocorrelations in non-linear time series with conditional heteroscedasticity. Journal of Time Series Analysis 15, 627–36.
  • $\begingroup$ Thanks so much again, Richard Hardy. You were absolutely right, I did not use standardized residuals. Now I squared and estimated those again and, well, those are basically white noise according to Bartlett's periodogram-based test for white noise as well as Portmanteau (Q) test for white noise. Therefore no autocorrelation and thus no GARCH effects possible. One question remains: Which model should I prefer - the one with the ARMA mean equation or just the no conditional mean GARCH model? $\endgroup$
    – Taufi
    Mar 1, 2016 at 18:14
  • $\begingroup$ You could compare the information criteria (AIC, BIC) of the two models and choose the one with lower values. You could also look at autocorrelations of non-squared standardized residuals (less autocorrelation is better), but perhaps you have already done that by conducting the Portmanteau (Q) test. $\endgroup$ Mar 1, 2016 at 19:04

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