Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors

Abstract

The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric values, an Edgeworth expansion of the bootstrap t-statistic of arbitrarily large order of the process is proved to have an error of o(n1-s/2) where s is a positive integer. The result is similar to the Edgeworth expansion obtained by Andrews and Lieberman [2002], which was established for the parametric bootstrap t-statistic of the plug-in maximum likelihood (PML) estimators of stationary, Gaussian, and strongly dependent processes, but without the linear regression component.

Keywords

• Edgeworth Expansion; parametric bootstrap; t-statistic
• linear regression
• strongly dependent