Reexamining an old story: uncovering the hidden small sample bias in AR(1) models

The first order autoregressive [AR(1)] model is widely used to investigate psycholog- ical dynamics. This study focuses on the estimation and inference of the autoregressive (AR) effect in AR(1) models under a limited sample size—a common scenario in psy- chological research. State-of-the-art estimators of the autoregressive effect are known to be biased when sample sizes are small. We analytically demonstrate the causes and consequences of this small sample bias on the estimation of the AR effect, its variance, and the AR(1) model’s intercept, particularly when using OLS. In addition, we reviewed various bias correction methods proposed in the time series literature. A simulation study compares the OLS estimator with these correction methods in terms of estimation accuracy and inference. The main result indicates that the small sam- ple bias of the OLS estimator of the autoregressive effect is a consequence of limited information and correcting for this bias without more information always induces a bias-variance trade-off. Nevertheless, correction methods discussed in this research may offer improved statistical power under moderate sample sizes when the primary research goal is hypothesis testing.