In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression 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 order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number
2000-12.
Find related papers by JEL classification: C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
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