Прогнозирование временных рядов методом скрытых марковских моделей

Abstract

A non-standard method for analyzing and forecastingmedical and social time series, namely the Hidden Markov Models method (HMM), is considered. The basic theoretical principles of mathematical apparatus of Markov chains and HMM are presented, the application limitations of forecasting method based on the Markov model of time series, its advantages and disadvantages are analyzed. The time series were tested for stationarity using the Augmented Dickey – Fuller test. The procedure of constructing the Hidden Markov Model for the time series of the first differences and the method for obtaining the predicted value are considered. A 3 х 3 – HMM model for the time series of the first differences is built. The hidden states of the model are obtained as a result of the Cluster Analysis procedure, an alphabet is constructed for theiridentification.