Forecasting autoregressive time series with bias-corrected parameter estimators

Abstract

The parameter estimators of autoregressive (AR) models are biased in small samples, and these biases can adversely affect their forecast accuracy. The purpose of this paper is to evaluate the effect of bias-correction for AR parameter estimators on forecast accuracy. The bias-corrected parameter estimators considered include a bootstrap mean bias-corrected estimator similar to [ The Review of Economics and Statistics, 80 (1998) 218], the bootstrap approximately median bias-corrected estimator, the modified estimator of [ Journal of Business & Economic Statistics, 19(4) (2001) 482], and the approximately median-unbiased estimator of [ Journal of Business & Economic Statistics, 12 (1994) 187]. Monte Carlo simulations are conducted for AR models with linear time trend. It is found that all bias-corrected estimators can deliver a substantial gain of forecast accuracy for unit root or near-unit root AR models, especially when the sample size is small. Overall, the bootstrap mean bias-corrected estimator is found to provide more accurate forecasts than the other alternatives over a wider range of the parameter space.