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Edgeworth Expansion of the t-statistic for Linear Regression Processes with Long-memory Errors

Mosisa Aga


The purpose of this paper is to provide a valid Edgeworth expansion for the t-statistic of a linear regression process whose error terms are stationary, Gaussian, and long-memory time series. Under some sets of conditions on the spectral density function and the parametric values, an Edgeworh expansion of of the t-statistic of arbitrarily large order of the process is proved to have an error of o where s is a positive integer. The result is similar to the asymptotic expansion obtained by O. Lieberman, J. Rousseau, and D.M. Zacker (2003),which was established for the PML estimators of stationary, Gaussian, and strongly dependent processes, and to that of Andrews and Lieberman [2002], which was established for the t-statistic of the same process without the linear regression component.


t-statistic, Edgeworth expansion, Gaussian process, linear regression model, long memory process, maximum likelihood estimator, plug-in likelihood function.

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