Hi,I am reading a chapter on 'Estimating Volatilities and Correlations' [Options, Futures, ... by John Hull] which provides an introduction to Garch model.In one section the author shows how good a given garch model by calculating the autocorrelation structure of the square of the return variable.Specifically, assume Ui and Oi^2 are the daily return and daily variance [of the return] on day i respectively. Also assume the mean of the daily return is 0, i.e. E[Ui] = 0Now suppose Oi^2 is constructed/estimated using the Garch model. The author states that we can estimate how good the model is by calculating the autocorrelation of the variable Y = Ui^2 / Oi^2He says that if the autocorrelation of variable Y is small/negligible, it means that our model for Oi^2 has succeeded in explaining autocorrelations in the Ui^2.Can someone kindly explain to me what he actually means?Thanks a lot in advance.Regards,L

The GARCH model starts with:where the epsilon's are IID white noise (uncorrelated), and sigma^2 follows the GARCH equation.Hence, , where the bar is now a fitted value.Thus if our model is good this should give an uncorrelated sequence.Also, you want the r_t above to be uncorrelated -- otherwise first fit something like an ARIMA to the returns and then model garch to the errors of the ARIMA.Basically for the standard GARCH the series is uncorrelated but the square of the series does have serial correlation, so if the GARCH model is fitting this correlation, dividing it out should leave you with something uncorrelated.

I wud like to make a small improvement. fitted epsilon values have to be Independent NOT only uncorrelated.Regards,

I suppose, but is that really a big deal ? The standard residual test (e.g. Ljung-Box) just test for autocorrelation -- which is what the original poster also mentioned. Would having possibly dependent but uncorrelated errors mess up certain statistics?

Thanks for your replies guys!Regards,L