On asymptotic distributions of weighted sums of periodograms

Giraitis, Liudas and Koul, Hira L. (2013) On asymptotic distributions of weighted sums of periodograms. Bernoulli, 19 (5B). pp. 2389-2413. ISSN 1350-7265

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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.

Item Type:	Article
Official URL:	http://www.bernoulli-society.org/index.php/publica...
Additional Information:	© 2013 ISI/BS
Divisions:	Economics
Subjects:	Q Science > QA Mathematics
Date Deposited:	06 Aug 2014 08:12
Last Modified:	14 Sep 2024 06:10
URI:	http://eprints.lse.ac.uk/id/eprint/58685

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