COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1367

Local Whittle Estimation of Fractional Integration

Katsumi Shimotsu and Peter C. B. Phillips

May 2002
Updated July 2004

An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0,1/4) limit distribution for all values of d if the optimization covers an interval of width less than 9/2 and the initial value of the process is known.

Keywords: Discrete Fourier transform, Fractional integration, Long memory, Nonstationarity, Semiparametric estimation, Whittle likelihood

JEL Classification: C22