engleski

A Methodology for the Identification of Periodicities in Two-dimensional Time Series

A new technique to identify periodicities in two-dimensional movements has been investigated. As a typical example, polar motion is approximated by complex-valued series. The detected frequencies do not have to show integer ratios among themselves as in Fourier series ; they can assume arbitrary real values. The fitting of the parameters of frequency series to the polar motion data results from a least-squares adjustment in which not only the amplitudes, but the frequencies as well are considered as unknowns. The approximate values for the frequencies in this severely nonlinear adjustment problem are obtained by a heuristic procedure. In doing so there is no need for prior information regarding individual possibly occurring frequencies. The methodology is illustrated by the Earth Orientation Parameter series C01 (EOP-C01) of the International Earth rotation and Reference system Service (IERS). The determined annual and Chandler frequencies lie inside the intervals determined by other authors using other techniques. However, since the frequencies determined by the new technique are not restricted to some set of Fourier-like frequencies, an interpretation of them as existing in the reality is less artificial. Therefore, the presented technique represents an expansion of the up to now available inventory of methods and can be successfully applied for the determination of frequencies contained in two-dimensional data. The advantages of the proposed procedure are that it can be easily generalized for the analysis of any time series of arbitrary dimensions and that even the data gaps within the analyzed time series would generate no theoretical or numerical difficulties.

Identification of periodicities; Frequency analysis; Global optimization; Two-dimensional time series; Ar

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