CFDP 1266

Local Whittle Estimation in Nonstationary and Unit Root Cases

Author(s): 

Publication Date: July 2000

Revision Date: June 2003

Pages: 33

Abstract: 

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.

Keywords: 

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

JEL Classification Codes:  C22

See CFP: 1098