In time series analysis, it is often important to determine the optimum number of lags in order to remove serial correlation. For example, in VAR, Dickey-Fuller unit-root test or Granger causality test, and many other models. This is usually done using information criteria such as Akaike, Bayesian or Hannan-Quinn information criterion.
Are there any rules about which criterion should be applied to a series based on how the series looks and the properties it has or based on what we can assume about variables from the economic theory? Or should all be used and decisions be made based on results from most of them? Are there some situations where some criteria are biased while others are not?
I already asked this question on Economics.SE but did not get any answer so I am trying here as well.