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Testing for the presence of sinusoidal components

Published online by Cambridge University Press:  14 July 2016

Abstract

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.

Type
Part 3—Hypothesis Testing and Distribution Theory for Time Series
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Fisher, R. A. (1929) Tests of significance in harmonic analysis. Proc. R. Soc. London A 125, 5459.Google Scholar
Hannan, E. J. (1961) Testing for a jump in the spectral function. J. R. Statist. Soc. B 23, 394404.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Priestley, M. B. (1962) Analysis of stationary processes with mixed spectra–II. J. R. Statist. Soc. B 24, 511529.Google Scholar
Priestley, M. B. (1981) Spectral Analysis and Time Series. Academic Press, London.Google Scholar
Walker, A. M. (1965) Some asymptotic results for the periodogram of a stationary time series. J. Austral. Math. Soc. 5, 107128.CrossRefGoogle Scholar
Walker, G. T. (1914) Correlation in seasonal variation of weather. III. On the criterion for the reality of relationships or periodicities. Mem. Indian Metereol. Dept. 21 (9), 1315.Google Scholar
Whittle, P. (1952) The simultaneous estimation of a time series' harmonic components and covariance structure. Trab. Estadist. 3, 4357.Google Scholar