Finite Sample Properties of Several Predictors From an Autoregressive Model

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to <italic>O</italic>(<italic>T</italic>⁻¹), where <italic>T</italic> is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to <italic>O</italic>(<italic>T</italic>⁻¹).