Analysis of correlations between time series with the use of the phase spectrum |
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| Authors: | M I Fortus |
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| Institution: | (1) Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017, Russia |
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| Abstract: | In connection with the problem of revealing cause-effect relations among different climatic characteristics, methods for determining the dependence between time series on the basis of selected auto-and cross-covariance functions and periodograms expressed in terms of the Fourier coefficients of the initial series are discussed. Real time series do not always satisfy the conditions of statistical stationarity, so that their analysis requires a combination of statistical and deterministic approaches. The possibility of using the above numerical characteristics in relation to such series is considered. Characteristic features of describing finite segments of time series with the use of their Fourier coefficients is studied in detail. The main emphasis is on the determination of the time shifts (delays) at which the covariance between the series is maximal. The problems that appear during a practical implementation of the periodogram method for shift estimation are discussed. A previously unknown formula that is necessary for further studies and relates the Fourier transform of a selected correlation function to the periodogram of the series is derived. |
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