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Suppose I fit a GARCH(1,1) model with Student-$t$ innovations of the standardized residuals using BIC selection. My mean model is ARMA(0,0). What can I do when the standardized residuals are still correlated?

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Try changing the model specification.

  • The most obvious first step is to try a different conditional mean model, e.g. an ARMA($p,q$) with $p>0$ or $q>0$, or both.
  • Alternatively, try changing the specification of the conditional variance model or the distribution of the standardized innovations. Tweaking one or both of the latter will also change the correlation structure of the standardized innovations.

It is difficult to propose anything more concrete at this stage; I think you just have to play around with the model specification and see what you get.

Note also that the null distribution and the corresponding critical values of autocorrelation tests such as Ljung-Box need to be adjusted if you apply the test on model residuals rather than raw data.

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  • $\begingroup$ Awesome suggestion, I try fitting different mean models and selected using AIC/BIC and it works. The residuals turn out uncorrelated. I want to add some words so that whoever having the same issue can see this. I extracted the "Correlated" standardized residuals and plot ACF and PACF graph to get some insight of the parameter P and Q in the mean model. pretty much like the case in linear time series. Thank Richard once again ! $\endgroup$
    – Zel Wei
    Commented Dec 14, 2017 at 4:12
  • $\begingroup$ @ZelWei, thanks! Be aware that you may accept the answer by clicking on the tick mark to the left. If the answer is not satisfactory, you need not accept it. This is how Cross Validated works. $\endgroup$ Commented Dec 14, 2017 at 6:06
  • $\begingroup$ Alright, thanks for being my 1st respondent, glad to have you answered. I am still new here, cheers! $\endgroup$
    – Zel Wei
    Commented Dec 14, 2017 at 9:47

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