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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Consistency of the least squares estimator of the amplitudes and angular frequencies of a sum of harmonic oscillations in models with long-range dependence


Author: A. V. Ivanov
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal: Theor. Probability and Math. Statist. 80 (2010), 61-69
MSC (2000): Primary 62J02; Secondary 62J99
Published electronically: August 18, 2010
MathSciNet review: 2541952
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Abstract: The strong consistency of least squares estimators of unknown amplitudes and angular frequencies of the sum of harmonic oscillations observed in a strongly dependent Gaussian stationary noise is proved in the paper.


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Additional Information

A. V. Ivanov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue 37, Kiev 03056, Ukraine
Email: ivanov@paligora.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2010-00794-0
PII: S 0094-9000(2010)00794-0
Keywords: The detection of hidden periodicities, least squares estimator, consistency, long range dependence
Received by editor(s): September 11, 2008
Published electronically: August 18, 2010
Article copyright: © Copyright 2010 American Mathematical Society