An Asymptotic Theory of Bayesian Inference for Time Series

A limiting representation of the Bayesian data density is obtained and shown to be the same general exponential form for a wide class of likelihoods and prior distributions. An embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the embedding, the authors obtain a large sample approximation to the model of the data that corresponds to the exponential density. This has the form of discrete observations drawn from a nonlinear stochastic differential equation driven by Brownian motion. No assumptions concerning stationarity or rates of convergence are required in the asymptotics. Some implications for statistical testing are explored. Copyright 1996 by The Econometric Society.