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Hidden Frequency Estimation with Data Tapers
Author(s) -
Chen ZhaoGuo,
Wu Ka Ho,
Dahlhaus Rainer
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00177
Subject(s) - mathematics , periodogram , estimation , series (stratigraphy) , noise (video) , spectral density estimation , algorithm , time series , estimation theory , statistics , pattern recognition (psychology) , computer science , artificial intelligence , mathematical analysis , fourier transform , paleontology , management , economics , image (mathematics) , biology
The detection and estimation of hidden frequencies has long been recognized as an important problem in time series. In this paper we study the asymptotic theory for two methods of high‐precision estimation of hidden frequencies (the secondary analysis method and the maximum periodogram method) using a data taper. In ordinary situations, a data taper may reduce the estimation precision slightly. However, when there are high peaks in the spectral density of the noise or other strong hidden periodicities with frequencies close to the hidden frequency of interest, the procedures for detection of the existence of and estimation of the hidden frequency of interest fail if data are nontapered whereas they may work well if the data are tapered. The theoretical results are verified by some simulated examples.