MULTIPLE LOCAL WHITTLE ESTIMATION IN STATIONARY SYSTEMS

• 成果类型: Article
• 署名作者: Robinson, P. M.
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS545
• 发表日期: 2008
• 页码: 2508-2530
• 关键词: gaussian semiparametric estimation; central-limit-theorem; long-memory; time-series; FRACTIONAL COINTEGRATION; sample; NONSTATIONARY; regression; normality

摘要

Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter (gamma), at the frequency of principal interest. zeros for short-memory series gamma = 0 automatically. The latter case has also been stressed under long memory, along with the fractional differencing case gamma = (delta(2) - delta(1))pi/2, where delta(1), delta(2) are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the consequent properties of cross-autocovariances to ones of the (possibly bilateral) moving average representation which. with martingale difference innovations of arbitrary dimension, is used in asymptotic theory for local Whittle parameter estimates depending on a single smoothing, number. Incorporating also a regression parameter (beta) which, when nonzero, indicates cointegration, the consistency proof of these implicitly defined estimates is nonstandard due to the beta estimate converging faster than the others. We also establish joint asymptotic normality of the estimates, and indicate how this Outcome can apply in statistical inference on several questions of interest. Issues of implemention are discussed, along with implications of knowing beta and of correct or incorrect specification of gamma, and possible extensions to higher-dimensional systems and nonstationary series.