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Practical considerations in the study of spectral analysis of discrete processes

par Herteleer, Annie
Référence Journal of Interdisciplinary Cycle Research, 6, 3, page (223-240)
Publication Publié, 1975

Article révisé par les pairs

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Résumé :

The time series, studied e.g. in economics, biology, astronomy, constitute samples of stochastic processes Xt, having stationary or nonstationary characteristics. Through the spectral analysis of these processes and of the time series, one obtains more precise results than through the study made in the time domain. The use of spectral analysis permits a more precise determination of the cycles evidenced by the series. The processes considered in this paper are of finite moments of the first and second order. Certain essential characteristics of the phenomena under study may not appear if the latter present a trend in the mean. Therefore, the trend will be eliminated prior to any study. This is mostly done by using the technique of linear filtering, the effect of this operation on the spectrum being known. This allows one to consider E(Xt) = O, without prejudice to the generality of the study. Emphasis is put on the study of discrete processes. Comparisons are made between results obtained for discrete processes and those obtained for continuous processes.