Fitting autoregressive trend stationary models with finite samples

Sims conjectured that the conditional maximum likelihood estimator of autoregressive trend stationary models of macroeconomic time series will tend to place initial observations relatively far from the estimated trend line, explaining early sample behavior as transient behavior as these series move from their extreme initial positions back toward the trend path. This can be misleading if the entire sample has been generated by the same data generating process and there is nothing unusual about the initial observations. We use Monte Carlo methods and the extended Nelson–Plosser data set to evaluate Sims' conjecture. We also study the behavior of the weighted symmetric estimator developed by Park and Fuller as an estimator of autoregressive trend stationary models.