The Size and Power of the Bias-Corrected Bootstrap Test for Regression Models with Autocorrelated Errors

Abstract

This paper is concerned with statistical inference for the coefficient of the linear regression model when the error term follows an autoregressive (AR) model. Past studies have reported severe size distortions, when the data are trending and autocorrelation of the error term is high. In this paper, we consider a test based on the bias-corrected bootstrap, where bias-corrected parameter estimators for the AR and regression coefficients are used. For bias-correction, the jackknife and bootstrap methods are employed. Monte Carlo simulations are conducted to compare size and power properties of the bias-corrected bootstrap test. It is found that the bias-corrected bootstrap test shows substantially improved size properties and exhibits excellent power for most of cases considered. It also appears that bootstrap bias-correction leads to better size and higher power values than jackknife bias-correction. These results are found to be robust to the choice of parameter estimation methods.