This paper oﬀers a general approach to time series modeling that attempts to reconcile classical and methods. The central idea put forward to achieve reconciliation is that the Bayesian approach relies implicitly a frame of reference for the data generating mechanism that is quite diﬀerent from the one that is employed in the classical approach. Diﬀerences in inferences from the two approaches are therefore to be expected unless the altered frame reference is taken into account. We show that the new frame of reference in Bayesian inference is a consequence of a change of measure that arises naturally in the application of Bayes theorem. Our paper explores this change of measure and its consequences using martingale methods. Examples are give illustrate its practical implications. No assumptions concerning stationarity or rates of convergence are required and techniques of stochastic diﬀerential geometry on manifolds are involved. Some implications for statistical testing are explored and suggest new tests, which we call Bayes model tests, for discriminating between models.
Phillips, Peter C.B. and Ploberger, Werner, "Time Series Modelling with a Bayesian Frame of Reference: I. Concepts and Illustrations" (1991). Cowles Foundation Discussion Papers. 1223.