Local Whittle estimation of the long-memory parameter

In this article, we describe and implement the local Whittle and exact local Whittle estimators of the order of fractional integration of a time series.

EXACT LOCAL WHITTLE ESTIMATION IN LONG MEMORY TIME SERIES WITH MULTIPLE POLES

A generalization of the Exact Local Whittle estimator in Shimotsu and Phillips (2005, Annals of Statistics 33, 1890–1933) is proposed for jointly estimating all the memory parameters in general long memory time series that possibly display standard, seasonal, and/or other cyclical strong persistence. Consistency and asymptotic normality are proven for stationary, nonstationary, and noninvertible series, permitting straightforward standard inference of interesting hypotheses such as the existence of unit roots and equality of memory parameters at some or all seasonal frequencies, which can be used as a prior test for the application of seasonal differencing filters. The effects of unknown deterministic terms are also discussed. Finally, the finite sample performance is analyzed in an extensive Monte Carlo exercise and an application to an U.S. Industrial Production index.