COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1587

Log Periodogram Regression: The Nonstationary Case

Chang Sik Kim and Peter C.B. Phillips

October 2006

Estimation of the memory parameter (d) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.

Keywords: Discrete Fourier transform, Fractional Brownian motion, Fractional integration, Inconsistency, Log periodogram regression, Long memory parameter, Nonstationarity, Semiparametric estimation

JEL Classification: C22