An Algorithm for Analysis of Multidimensional Time Series with Smoothly Varying Regularities and Its Application

A new approach to revealing regularities in nonstationary k-valued multidimensional time series is proposed. It allows one to discover regularities that are subject to gentle structural changes with time. A measure of similarity between regularities is proposed to describe such changes, and its application in the form of weight in the graph of regularities is discussed. The discovered regularities can be used to predict the subsequent elements in multidimensional time series, to analyze the phenomenon described by this series, and to model the phenomenon. This allows one to use the proposed algorithm in a wide variety of problems concerning prediction of time series and for examining and describing the processes that can be represented by multidimensional time series. Means for direct practical application of the proposed methods of the analysis and prediction of time series are described, and the use of these methods for short-term prediction of model series and a real-life multidimensional time series consisting of the stock prices of companies operating in similar fields is discussed. © 2010 Pleiades Publishing, Ltd.