# Why don't we look at $R^2$ when fitting an autoregressive model?

$R^2$ measures explained variance. In an autoregressive model like AR(k), we are carrying out a linear regression, and as such we would have an $R^2$ and an adjusted $R^2$. Why are they not used in practice?

IMHO, using the R2 is irrelevant since it would just push you to use a larger regression order $k$ which would generally give you a smaller R2. The idea of fitting an AR (or any GLP) is to reproduce the underlying process with a model that is as simple as possible (since the idea is also to extract meaning out of the different coefficients)
• I don't think this is entirely fair. Of course, when you measure performance on the same data as which you've fitted, there is a bias towards more and more complicated gives better results. However, also with auto-regression it makes a lot of sense to test on a separate set. Secondly, I would imagine that in most practical cases, you have to make a prediction at least $dt$ time ahead, enlarging ones look-back window will probably create better results, but not necessarily on the test set and they will likely have an elbow somewhere. – Herbert Nov 15 at 13:15