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November 2013 On asymptotic distributions of weighted sums of periodograms
Liudas Giraitis, Hira L. Koul
Bernoulli 19(5B): 2389-2413 (November 2013). DOI: 10.3150/12-BEJ456

Abstract

We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions of quadratic forms involving integrals of weighted periodograms. Conditions for asymptotic normality of these weighted sums are simple, minimal, and resemble Lindeberg–Feller condition for weighted sums of independent and identically distributed random variables. Our results are applicable to a large class of short, long or negative memory processes. The proof is based on sharp bounds derived for Bartlett type approximation of these sums by the corresponding sums of weighted periodograms of independent and identically distributed random variables.

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Liudas Giraitis. Hira L. Koul. "On asymptotic distributions of weighted sums of periodograms." Bernoulli 19 (5B) 2389 - 2413, November 2013. https://doi.org/10.3150/12-BEJ456

Information

Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1280.62112
MathSciNet: MR3160558
Digital Object Identifier: 10.3150/12-BEJ456

Keywords: Bartlett approximation , Lindeberg–Feller , linear process , Quadratic forms

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 5B • November 2013
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