Method of the Cyclic Decomposition for Revealing the Latent Periodicity in Numerical Rows

Abstract

A new mathematical approach - method of cyclic decomposition (CD) the has been developed for search of the latent periodicity in numerical rows. The given method is generalization of a method of the information decomposition (ID) developed earlier for symbolical sequences. Quantitative measure of periodicity is the nonparametric statistics counted by criterion of series. The method of cyclic decomposition, as well as a method of information decomposition, is capable to determine strongly dim periodicity in numerical sequences which cannot be found out by means of other known mathematical methods, in particular Fourier transformation. Examples of applications of method CD for the analysis of artificial numerical rows and time series of the financial nature are shown.