EXACT LOCAL WHITTLE ESTIMATION IN LONG MEMORY TIME SERIES WITH MULTIPLE POLES
将精确局部Whittle估计推广到一般长记忆时间序列，可同时估计标准、季节和周期性的多个记忆参数，并证明了平稳、非平稳和不可逆序列下估计的一致性和渐近正态性，适用于单位根检验和季节频率记忆参数相等性检验。
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.