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Semiparametric analysis of long memory time series

Robinson, Peter (1994) Semiparametric analysis of long memory time series. Annals of Statistics, 22 (1). pp. 515-539. ISSN 0090-5364

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Identification Number: 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

Item Type: Article
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Divisions: LSE
Date Deposited: 27 Apr 2007
Last Modified: 15 Sep 2023 12:13

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