Edgeworth Expansion for the Whittle Maximum Likelihood Estimator of Linear Regression Processes with Long Memory Residuals

We establish an Edgeworth expansion for the distribution of the Whittle maximum likelihood estimator of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory residuals. This is done by imposing an extra condition on coefficients of the regression model in addition to the standard conditions imposed on the the spectral density function and the parameter values and making use of the results of Andrews et al. (2005), who provided an Edgeworth expansion for the residual component.