Errors and residuals

Is there a difference between error autocorrelation and residuals autocorrelation? I thought errors and residuals are the same thing (difference between predicted Y and observed Y). Are the errors from a population and residuals from a sample?

Where did you see these two expressions???

Don’t know the exact page in the CFAI texts. It is in reading 13 regarding time-series autoregression testing. I don’t have my books in front of me but if I recall, the text says something to the matter of “to test for an AR model, we checking for error autocorrelation bu checking the residual autocorrelation between independent and residuals.” edit: if anyone has their texts around, I think it’s the second page in the discussion of AR. It is about halfway down and the words “error autocorrelation” and “residual autocorrelation” are highlighted in bolded blue.

Error autocorrelation is about the actual model. Residual autocorrelation is what you get when you fit the model and look at the residuals from your fit. It would be really nice if the estimate of autocorrelation for residuals was a good estimator for the autocorrelation of the errors…

So, Error autocorrelation refers to the population? and Residual autocorrelation refers to the sample? Is that it?

Kind-of, but it’s not completely clean like mu and X-bar because the errors aren’t really parameters. So suppose that you are doing a regression model on Y(t) = A + B*X(t) + e(t) where Y(t) = measure of some pollutant in the air and X(t) = # cars that cross some bridge on day t. You would expect the errors to be autocorrelated because pollution lingers. A bad pollution day on Wednesday contributes to a bad pollution day on Thursday. The e(t)'s are your error terms and if you just do a straight regression you haven’t modeled them at all (except in the default way of saying they are independent). So now you fit a regression and get a bunch of residuals r(t) = Y(t) - A-hat - B-hat*X(t). If your errors are independent then your r(t)'s are independent and you can use the observed distribution of r(t) to say a lot about the unobserved distribution of e(t). Of course, if the e(t)'s are correlated so will the r(t)'s and, in particular, since the e(t)'s are positively correlated you will underestimate the error variance using the distribution of r(t).

Got it. Thanks JDV.