The Annals of Statistics

Small Sample Effects in Time Series Analysis: A New Asymptotic Theory and a New Estimate

Rainer Dahlhaus

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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.

Article information

Source
Ann. Statist. Volume 16, Number 2 (1988), 808-841.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350838

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176350838

Mathematical Reviews number (MathSciNet)
MR947580

Zentralblatt MATH identifier
0662.62100

Subjects
Primary: 62M15: Spectral analysis
Secondary: 62F10: Point estimation

Keywords
Small sample effects time series data tapers Whittle estimates maximum likelihood estimates

Citation

Dahlhaus, Rainer. Small Sample Effects in Time Series Analysis: A New Asymptotic Theory and a New Estimate. The Annals of Statistics 16 (1988), no. 2, 808--841. doi:10.1214/aos/1176350838. http://projecteuclid.org/euclid.aos/1176350838.


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