Modeling of Time Series with Structural Discontinuities Based on Fuzzy Markov Chains

In this paper, multidimensional time series with structural discontinuities or disorder are considered. A structural break or disorder is understood as a change in the parameters of the process behavior model or the parameters of the distribution of a random component. The aim of the study is to build an autoregression model with variable coefficients that take into account structural gaps. Modeling of such a time series is implemented on the basis of fuzzy Markov chains. The technique is based on the transformation of a numerical time series into a random sequence of categorical fuzzy states. The considered approach makes it possible to solve the general scientific problem of modeling a time series with implicit changes in properties and significantly improve the quality of the model compared to the known ones.