COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1244

Unit Root Log Periodogram Regression

Peter C.B. Phillips

December 1999

Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d = 1. Gaussian errors are not required. Tests of d = 1 based on LP regression are consistent against d < 1 alternatives but inconsistent against d > 1 alternatives. A test based on a modified LP regression that is consistent in both directions is provided.

Keywords and phrases: Discrete Fourier transform, fractional Brownian motion, fractional integration, log periodogram regression, long memory parameter, nonstationarity, semiparametric estimation and testing, unit root.