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Estimation of Trigonometric Components in Time Series

E. Damsleth and E. Spjotvoll
Journal of the American Statistical Association
Vol. 77, No. 378 (Jun., 1982), pp. 381-387
DOI: 10.2307/2287255
Stable URL: http://www.jstor.org/stable/2287255
Page Count: 7
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Estimation of Trigonometric Components in Time Series
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Abstract

Estimation in time series with an unknown number of deterministic trigonometric components with unknown amplitudes and frequencies is considered. A stepwise procedure is used. At each step the frequency of the largest term in the periodogram of the residual series is used as a starting value for finding the best frequency in the least squares sense. The procedure is stopped when there are no further significant harmonic components, when tested by a multiple-test procedure. The fitting procedure is tried on various time series, including the sunspot series. For long-term prediction the deterministic model does better for the sunspot series than, for example, autoregressive models.

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