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June, 1995 Log-Periodogram Regression of Time Series with Long Range Dependence
P. M. Robinson
Ann. Statist. 23(3): 1048-1072 (June, 1995). DOI: 10.1214/aos/1176324636


This paper discusses the estimation of multiple time series models which allow elements of the spectral density matrix to tend to infinity or zero at zero frequency and be unrestricted elsewhere. A form of log-periodogram regression estimate of differencing and scale parameters is proposed, which can provide modest efficiency improvements over a previously proposed method (for which no satisfactory theoretical justification seems previously available) and further improvements in a multivariate context when differencing parameters are a priori equal. Assuming Gaussianity and additional conditions which seem mild, asymptotic normality of the parameter estimates is established.


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P. M. Robinson. "Log-Periodogram Regression of Time Series with Long Range Dependence." Ann. Statist. 23 (3) 1048 - 1072, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0838.62085
MathSciNet: MR1345214
Digital Object Identifier: 10.1214/aos/1176324636

Primary: 62M10
Secondary: 60G18 , 62G05

Keywords: $\log$-periodogram regression , generalized least squares , least squares , limiting distribution theory , Long range dependence

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
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