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February 1997 Time series regression with long-range dependence
P. M. Robinson, F. J. Hidalgo
Ann. Statist. 25(1): 77-104 (February 1997). DOI: 10.1214/aos/1034276622


A central limit theorem is established for time series regression estimates which include generalized least squares, in the presence of long-range dependence in both errors and stochastic regressors. The setting and results differ significantly from earlier work on regression withlong-range-dependent errors. Spectral singularities are permitted at any frequency. When sufficiently strong spectral singularities in the error and a regressor coincide at the same frequency, least squares need no longer be $n^{1/2}$-consistent, where n is the sample size. However, we show that our class of estimates is $n^{1/2}$-consistent and asymptotically normal. In the generalized least squares case, we show that efficient estimation is still possible when the error autocorrelation is known only up to finitely many parameters. We include a Monte Carlo study of finite-sample performance and provide an extension to nonlinear least squares.


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P. M. Robinson. F. J. Hidalgo. "Time series regression with long-range dependence." Ann. Statist. 25 (1) 77 - 104, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0870.62072
MathSciNet: MR1429918
Digital Object Identifier: 10.1214/aos/1034276622

Primary: 60G18, 62M10
Secondary: 62F12, 62J02, 62J05

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • February 1997
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