Broadband log-periodogram regression of time series with long-range dependence

• 成果类型: Article
• 署名作者: Moulines, E; Soulier, P
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite Paris Saclay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1415-1439
• 关键词: variables

摘要

This paper discusses the properties of an estimator of the memory parameter of a stationary long-memory time-series originally proposed by Robinson. As opposed to narrow-band estimators of the memory parameter (such as the Geweke and Porter-Hudak or the Gaussian semiparametric estimators) which use only the periodogram ordinates belonging to an interval which degenerates to zero as the sample size n increases, this estimator builds a model of the spectral density of the process over all the frequency range, hence the name, broadband. This is achieved by estimating the short-memory component of the spectral density, f*(x) = \1 - e(ix)\(2d)f(x), where d is an element of (-1/2,1/2) is the memory parameter and f(x) is the spectral density, by means of a truncated Fourier series estimator of log f*. Assuming Gaussianity and additional conditions on the regularity of fb which seem mild, we obtain expressions for the asymptotic bias and variance of the long-memory parameter estimator as a function of the truncation order. Under additional assumptions, we show that this estimator is consistent and asymptotically normal. If the true spectral density is sufficiently smooth outside the origin, this broadband estimator outperforms existing semiparametric estimators, attaining an asymptotic mean-square error O(log(n)/n).