How to test homoscedasticity when the errors are DEPENDENT?

Question

I have done a linear regression and plot the residuals. I noticed that the errors are dependent(autocorrelated), how could I test homoscedasticity of this series? I read that Breusch-Pagan test only work with independent errors.

What test could I use to test if the variance is constant in this case?

• IrishStat: augment your under-specified model with arima structure to render a set of errors that are uncorrelated and then consider testing for points in time where the error variance changes.

Answer 1

IrishStat gave a good comment that points to an answer. He isn't on the site any more, so I will attempt an answer.

If you have autocorrelated errors, then you have to fix those before you worry about heteroscedasticity. One way to attempt to do this is as IrishStat suggests: Don't use linear regression; use ARIMA (or another time series method). Or, if you have a short time series, you could try a multilevel model or generalized estimating equations (GEE).

All of those methods have been discussed a lot here, and there is also a huge literature about them.