We have to test for serial correlation in an AR model by seeing if autocorrelations are significant because we can’t use the DW test for AR models. I get that.
From volume 1, pg 415: “The autocorrelations of a time series are the correlations of that series with its own past values”. Why is this a bad thing? If an AR model regresses its own past values, there HAS to be some correlation?
And finally to correct for autocorrelation we keep adding a lag to the AR§ model. How does more lag reduce the autocorrelations?
“The autocorrelations of a time series are the correlations of that series with its own past values”. Why is this a bad thing?
Objectives of quant models:
1)Express a relationship in number of variables.
Reduce the error term values ( Unexplained variation is not desiable).
Models with autocorrelation has relation with their past which is represented in error term (which hasn’t expressed by their indepdent variable) so your model is still incomplete. That’s the reason serial correlation is bad.
I think you are confused about the independent variable and the error terms. Look, to construct an AR model the variable (let’s say X) needs to be autocorrelated (correlated with its own past), if not so why build an AR model?
But what must not be autocorrelated are the errors resulting of that model, the model errors must not have significant autocorrelations for many past times. If it were the case, your model is incorrectly specified and must not be used. Thats why you look on the lag autocorrelation of ERRORS , not the variable itself. If there are significant autocorrelations, it means that your model (let’s say an AR(1) model) is not good enough. Those autocorrelations of errors can spot you the place of the missed variable, for example if you have the lag autocorrelation of error number 4 being significant, it means that your model is not accounting for a lag number 4 of the X variable, so you add an X(t-4) in your model and that autocorrelation significance is expected to desappear telling you that the model is correctly specified now.