COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1266

Local Whittle Estimation in Nonstationary and Unit Root Cases

Katsumi Shimotsu and Peter C.B. Phillips

July 2000
Revised June 2003

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

JEL Classification: C22

Key words: Discrete Fourier transform, fractional Brownian motion, fractional integration, long memory, nonstationarity, semiparametric estimation, trend, Whittle likelihood, unit root