КРИТЕРИЙ ДЛЯ ПРОВЕРКИ ГИПОТЕЗ О КОВАРИАЦИОННОЙ ФУНКЦИИ СИСТЕМЫ КВАЗИПЕРИОДИЧЕСКИХ ПРОЦЕССОВ, ПРЕДСТАВЛЕННЫХ ЦИЛИНДРИЧЕСКИМИ МОДЕЛЯМИ ИЗОБРАЖЕНИЙ

Abstract

The generally accepted mathematical model of a wide variety of natural, technical, economic and other objects that exist in time are random processes, for example sea waves, wind, vibrations of engines and hydraulic units, biorhythms, etc. An object is usually described by several parameters, that is a system of random processes or time series. The processes occurring in many objects have a form close to periodic – quasiperiodic, namely there is a periodicity with an element of unpredictability, for example speech sounds, vibrations of various technical objects, daily temperature fluctuations, etc. In order to formulate the problems of processing the quasiperiodic process systems, their mathematical models are required. For this purpose, authors propose models in which the processes are presented in the form of spiral sweeps on autoregressive cylindrical images. A suitable set of parameter values for these models provides a given degree of quasiperiodicity of individual processes and the given covariance relationships between the processes of the system. A criterion is proposed for testing the hypotheses about the correspondence of the observed system of time series to their model of the described type. The authors provide the examples of the application of this criterion with an analysis of the sensitivity to deviations of the model parameters from the expected ones are given.