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June, 1988 Small Sample Effects in Time Series Analysis: A New Asymptotic Theory and a New Estimate
Rainer Dahlhaus
Ann. Statist. 16(2): 808-841 (June, 1988). DOI: 10.1214/aos/1176350838

Abstract

To estimate the parameters of a stationary process, Whittle (1953) introduced an approximation to the Gaussian likelihood function. Although the Whittle estimate is asymptotically efficient, the small sample behavior may be poor if the spectrum of the process contains peaks. We introduce a mathematical model that covers such small sample effects. We prove that the exact maximum likelihood estimate is still optimal in this model, whereas the Whittle estimate and the conditional likelihood estimate are not. Furthermore, we introduce tapered Whittle estimates and prove that these estimates have the same optimality properties as exact maximum likelihood estimates.

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Rainer Dahlhaus. "Small Sample Effects in Time Series Analysis: A New Asymptotic Theory and a New Estimate." Ann. Statist. 16 (2) 808 - 841, June, 1988. https://doi.org/10.1214/aos/1176350838

Information

Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0662.62100
MathSciNet: MR947580
Digital Object Identifier: 10.1214/aos/1176350838

Subjects:
Primary: 62M15
Secondary: 62F10

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 2 • June, 1988
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