Markovian processes, two-sided autoregressions and finite-sample inferencefor stationary and nonstationary autoregressive processes

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on speci al properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only requ ire the existence of conditional densities, They are proved for possibly no nstationary and/or non-Gaussian multivariate Markov processes, In the conte xt of a linear regression model with AR(1) errors, we show how these result s can be used to simplify the distributional properties of the model by con ditioning a subset of the data on the remaining observations, This transfor mation leads to a new model which has the form of a two-sided autoregressio n to which standard classical linear regression inference techniques can be applied, We show how to derive tests and confidence sets for the mean and/ or autoregressive parameters of the model. We also develop a test on the or der of an autoregression. We show that a combination of subsample-based inf erences can improve the performance of the procedure. An application to U.S . domestic investment data illustrates the method. (C) 2000 Elsevier Scienc e S.A. All rights reserved. JEL classification: C22; C32; C12; C5; E2; E22.