The Annals of Statistics

Limiting Behavior of Functionals of Higher-Order Sample Cumulant Spectra

Daniel MacRae Keenan

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Abstract

This paper is concerned with establishing a broad class of estimators (and the limiting behavior, thereof) for parametrizations of higher than second-order structure. This includes parametrizations which reflect, for example, such properties as nonlinearity and/or non-Gaussianity and/or time irreversibility. Asymptotic distributions, almost-sure convergence, and probability-one bounds for such estimators are established. Several applications of such estimators are discussed.

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 134-151.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350257

Digital Object Identifier
doi:10.1214/aos/1176350257

Mathematical Reviews number (MathSciNet)
MR885728

Zentralblatt MATH identifier
0682.62070

JSTOR
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 62M15: Spectral analysis

Keywords
Time series cumulant spectra functionals limiting behavior

Citation

Keenan, Daniel MacRae. Limiting Behavior of Functionals of Higher-Order Sample Cumulant Spectra. Ann. Statist. 15 (1987), no. 1, 134--151. doi:10.1214/aos/1176350257. https://projecteuclid.org/euclid.aos/1176350257


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