We are exploring the use of GARCH to estimate volatility. I've read several times that we should test for auto correlation to make sure that either the parameters make sense or that the underlying time series is applicable to GARCH use, but I'm not sure of exactly what data needs to be tested. I would assume that the very nature of GARCH is that we are depending on auto correlation since the predicted volatility is a function of yesterday's change as well as the series of prior changes.Any discussion on what time series needs to be tested and why would be appreciated.

You should review your time series or better yet, econometrics. If you are testing the data for autocorrelation, this does not imply that garch is applicable. It means the arma part of garch is applicable. You still need to perform the test for heteroskedasticity if you want to use garch.

Think the idea here is to test the (standardised) residuals for autocorrelation (and for normality)If the model is ok the residuals should be representative of white noise.GARCH typically removes some but not all of the heteroskedasticity Depending on your implementation you may be able to draw the innovations from a different distribution (the student t, for example) which may explain more of the information. You can check this using a qq-plot of the residuals for a normal distribution test.I think I can dig up some S-SPLUS code using the S+FinMetrics plug in which does stuff like this

Think the idea here is to test the (standardised) residuals for autocorrelation (and for normality)If the model is ok the residuals should be representative of white noise.GARCH typically removes some but not all of the heteroskedasticity Depending on your implementation you may be able to draw the innovations from a different distribution (the student t, for example) which may explain more of the information. You can check this using a qq-plot of the residuals for a normal distribution test.I think I can dig up some S-SPLUS code using the S+FinMetrics plug in which does stuff like this

Brian, are you saying that after I use GARCH and calibrate the parameters (alpha, beta and omega) I then test the residuals for auto correlation. If the residuals are not autocorrelated then I can feel comfortable that GARCH is giving reasonable approximations. This sounds good to me.Tabris, you also bring up a good point of testing the raw data series for heterskedastisity before using GARCH. What test would I run?I appreciate your feedback, this has already been helpful.

Combine what brian and outrun said and you should have somewhat of an adequate measure. Personally, I like to test the standardised residuals for autocorrelation (autoregressive part) and then test the squared of the residuals (conditional heteroskedasticity). To understand why you test the squared residuals, you can refer to Halbert White's paper on direct test for heteroskedasticity. I would also suggest using Ljung-Box instead of Durbin-Watson as Durbin-Watson only tests autocorrelation with lag = 1.