THE ROLE OF ANCILLARITY IN INFERENCE FOR NONSTATIONARY VARIABLES

Some examples of the regression method are compared with likelihood based inference. It is shown that although the asymptotic theory is distinctly different for ergodic and non-ergodic processes, the likelihood methods lead to the result that asymptotic inference can be conducted in the same way for the two cases by appealing to classical conditioning arguments from statistics using the notion of S-ancillarity or strong exogeneity. It is pointed out that the Fisher information can be considered a measure of the conditional variance of the maximum likelihood estimator given the available information in the sample.