MATLAB: How Should Conditional Mean and Variance Model be Changed if Residuals Exhibit Autocorrelation

Question

I have a time series Y that I know exhibits autocorrelation and heteroscedasticity. Using the estimate function, I fit a conditional mean and variance model to Y. I then use the infer function and get the residuals from the model fit to Y.

Two questions: 1) If the residuals exhibit autocorrelation, how should I change the conditional mean and variance model that was just fit (add more AR or MA lags?)? 2) If the residuals exhibit heteroscedasticity, how should I change the model (add more GARCH or ARCH terms to the variance model?)? Thank you.

Answer 1

It depends on the autocorrelation. If the autocorrelation occurs at a certain lag, then add a MA term at that lag. If the autocorrelation is a several lags, add AR terms. Another method is that you add AR and MA lags until the autocorrelation disapears. Check the T-values of the coefficients and remove those terms with insignificant coefficients. It is a bit of a trial-and-error process. Add terms and see if you can remove the autocorrelation. However, keep an eye on the T-values. The same process applies for removing the heteroscedasticity.