SEMIPARAMETRIC ANALYSIS OF LONG-MEMORY TIME-SERIES

• 成果类型: Article
• 署名作者: ROBINSON, PM
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325382
• 发表日期: 1994
• 页码: 515-539
• 关键词: stationary errors; range dependence; REGRESSION-MODEL; quadratic-forms; variables

摘要

We study problems of semiparametric statistical inference connected with long-memory covariance stationary time series, having spectrum which varies regularly at the origin: There is an unknown self-similarity parameter, but elsewhere the spectrum satisfies no parametric or smoothness conditions, it need not be in L(p), for any p > 1, and in some circumstances the slowly varying factor can be of unknown form. The basic statistic of interest is the discretely averaged periodogram, based on a degenerating band of frequencies around the origin. We establish some consistency properties under mild conditions. These are applied to show consistency of new estimates of the self-similarity parameter and scale factor. We also indicate applications of our results to standard errors of least squares estimates of polynomial regression with long-memory errors, to generalized least squares estimates of this model and to estimates of a ''cointegrating'' relationship between long-memory time series.