On Estimating Multimodal Spectra of Time Series

The estimates of multimodal spectra of random sequences are considered on an example of dendrochronological series (DCS). These series are representable as the sums of the tapered component, the spectrum of which then turns out to be proportional to the power of frequency with exponent $-\frac13$ and with several weakly manifested frequency maxima overlapping it. One can achieve a better manifestation of these maxima by considering the effects of moving tapering in time with various tapering windows and by constructing the spectra of the tapered series. In this way 7 maxima are detected with periods of about 2.7, 4.7, 23.7, 60, 120, 180, and 745 years.