Local Whittle estimation, fully extended for nonstationarity

K Abadir, W Distaso and Liudas Giraitis ()

Discussion Papers from Department of Economics, University of York

Abstract: We extend the classical local Whittle estimation procedure to fractionally integrated I(d) processes, where d>-3/2, thus covering stationary and non-stationary regions. Asymptotic properties of the bias of the estimator are investigated. It is shown that in a wider region than previously considered in the literature, the estimator exhibits the same asymptotic properties as in the stationary case. When the generating process is linear, existence of a Gaussian asymptotic distribution is shown. It is demonstrated that the estimator is consistent in the case of a signal plus noise process. Conditions characterizing trends which do not affect the consistency are provided and asymptotic properties of the estimator for detrended series are analysed. The performance of the estimator is illustrated by a simulation study.

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