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Consistent estimates for hidden frequencies in a linear process

Published online by Cambridge University Press:  01 July 2016

Chen Zhao-Guo
Chen Zhao-Guo*
Affiliation:
Institute of Applied Mathematics, Chinese Academy of Sciences
*
∗Postal address: Institute of Applied Mathematics, Academia Sinica, Beijing, China.
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Abstract

Traditional methods for detecting the hidden frequencies in white or coloured noise is based on the distribution of periodogram ordinates Ι (2πj/N) and hypothesis testing. The power is low when a hidden frequency falls midway between two 2nj/N and it is difficult to discuss the consistency of the procedures. Using theorems on almost sure convergence of the periodogram, this paper offers a procedure for detecting and estimating the hidden frequencies, and discusses the consistency and the rates of convergence. Simulation shows very good results, when the spectrum of the noise is not too steep.

Keywords

MAXIMUM OF THE PERIODOGRAMFEJER KERNELSTRONG CONSISTENCYLAW OF THE ITERATED LOGARITHMSECONDARY ANALYSIS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 295 - 314
Copyright
Copyright © Applied Probability Trust 1988 

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