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DETERMINING THE NUMBER OF TERMS IN A TRIGONOMETRIC REGRESSION
Author(s) -
Kavalieris L.,
Hannan E. J.
Publication year - 1994
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/j.1467-9892.1994.tb00216.x
Subject(s) - mathematics , autoregressive model , noise (video) , consistency (knowledge bases) , statistics , least squares function approximation , trigonometry , series (stratigraphy) , mathematical analysis , artificial intelligence , computer science , estimator , paleontology , geometry , image (mathematics) , biology
. We consider the estimation of the number of sinusoidal terms in a time series contaminated by additive noise with unknown correlation structure. The method fits sinusoidal terms by least squares and models the noise component using a high order autoregression. A criterion based on the minimum description length principle is used to select the number of sinusoidal terms and the order of the noise model. The small sample efficacy of the model selection procedure is examined by simulations and the analysis of some astronomical data. Consistency is proved under quite general conditions on the noise spectrum.