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Overlapped grouping periodogram test for detecting multiple hidden periodicities in mixed spectra
(with X. Wang and Q. Wen)
Journal of Time Series Analysis , 33(2), 2012, pp. 255-268
Abstract: Hidden periodicity is a featured phenomenon in many area of the real world, for example, in astronomy and climatology. Under white noise assumption, the problem of searching for hidden periodicity has been studied extensively in the literature. However, under mixed spectra, especially when compound periodicities are involved, most of the existing methods lose their efficiencies. An overlapped grouping periodogram (OGP) test is proposed in this paper to detect multiple hidden periodicities in mixed spectra. Its test statistic is proven to converge to Fisher's g-statistic almost surely. Difficulties arising from the implementation of the OGP test are tackled and an empirical data-adaptive confidence interval for grouping parameter selection is constructed when red noise is assumed. The large sample properties of the proposed OGP test are studied via Monte Carlo simulations, and the power of the test is further illustrated by applying it to the reanalysis of the monthly international sunspot series. By employing the new method, a 10-year cycle and an 11-year cycle are detected respectively in the monthly international sunspot series. These two cycles combined to form a super cycle with a period of about 110 years for the updated estimate to the solar cycle. The goodness of the OGP fit to the sunspot series is examined.
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