Consistency and asymptotic normality of the periodogram estimator of harmonic oscillation parameters

Authors:
A. V. Ivanov and B. M. Zhurakovskyi

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **89** (2013).

Journal:
Theor. Probability and Math. Statist. **89** (2014), 33-43

MSC (2010):
Primary 62J02; Secondary 62J99

DOI:
https://doi.org/10.1090/S0094-9000-2015-00933-9

Published electronically:
January 26, 2015

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Abstract | References | Similar Articles | Additional Information

Abstract: The problem of detection of hidden periodicities is considered in the paper. We study the model of the harmonic oscillation observed on the background of random noise being a local functional of a Gaussian strongly dependent stationary process. To estimate unknown angular frequency and amplitude of the harmonic oscillation, the periodogram estimator is chosen. Sufficient conditions of the asymptotic normality are found for the periodogram estimator and the limit normal distribution is determined.

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Additional Information

**A. V. Ivanov**

Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty of Physics and Mathematics, National Technical University of Ukraine, “Kiev Politechnic Institute”, Peremohy ave., 37, Kyiv 03056, Ukraine

Email:
alexntuu@gmail.com

**B. M. Zhurakovskyi**

Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty of Physics and Mathematics, National Technical University of Ukraine, “Kiev Politechnic Institute”, Peremohy ave., 37, Kyiv 03056, Ukraine

Email:
zhurak@gmail.com

DOI:
https://doi.org/10.1090/S0094-9000-2015-00933-9

Keywords:
Hidden periodicities,
periodogram estimator,
harmonic oscillation

Received by editor(s):
December 22, 2012

Published electronically:
January 26, 2015

Article copyright:
© Copyright 2015
American Mathematical Society