Random fluctuations, persistence, and quasi‐persistence in geophysical and cosmical periodicities

Publisher Website
Google Scholar
Abstract
The statistical aspects of the application of harmonic analysis, introduced by A. Schuster in his famous paper on the investigation of hidden periodicities, are discussed on the basis of recent developments in the theory of probability. Between the two extreme cases of random fluctuations and persistent waves, hitherto discussed exclusively, the intermediate case of quasi‐persistence is introduced and recognized as a common phenomenon in the time‐functions of meteorology, geophysics, and cosmical physics. Statistical methods, based on the conception of the harmonic dial, are given for dealing with quasi‐persistence and its effect on tests for persistent waves, and they are generalized for the case of periodicities of other form than that of the sine‐wave. Typical examples are given illustrating various forms of random fluctuations, quasi‐persistence, and persistence, as well as questions related to harmonic analysis, such as the periodogram, non‐cyclic change, curvature‐effect, equivalent length of sequences, effective expectancy, random walk, interference, and the infective property of quasi‐persistence on adjacent periods (see summary at end of paper).

This publication has 16 references indexed in Scilit: