Edgeworth expansion of the t-statistic of the whittle MLE for linear regression processes with long-memory disturbances

Abstract

This paper establishes an Edgeworth expansion for the t-statistic of the Whittle Maximum Likelihood Estimator (WMLE) of a linear regression model whose residual component is stationary, Gaussian, and strongly dependent time series. Under the widely used set of assumptions and two more mild additional conditions on the spectral density function and the parametric values, an Edgeworh expansion of the t-statistic of arbitrarily large order of the process is proved to have an error of o ( n 1 − s / 2 ) where s is a positive integer.