## The Annals of Statistics

### Time series regression with long-range dependence

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 25, Number 1 (1997), 77-104.

Dates
First available in Project Euclid: 10 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034276622

Digital Object Identifier
doi:10.1214/aos/1034276622

Mathematical Reviews number (MathSciNet)
MR1429918

Zentralblatt MATH identifier
0870.62072

#### Citation

Robinson, P. M.; Hidalgo, F. J. Time series regression with long-range dependence. Ann. Statist. 25 (1997), no. 1, 77--104. doi:10.1214/aos/1034276622. https://projecteuclid.org/euclid.aos/1034276622

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