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March, 1994 Semiparametric Analysis of Long-Memory Time Series
P. M. Robinson
Ann. Statist. 22(1): 515-539 (March, 1994). DOI: 10.1214/aos/1176325382


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.


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P. M. Robinson. "Semiparametric Analysis of Long-Memory Time Series." Ann. Statist. 22 (1) 515 - 539, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0795.62082
MathSciNet: MR1272097
Digital Object Identifier: 10.1214/aos/1176325382

Primary: 62M15
Secondary: 60G18, 62G05

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
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