HYBRID LINGUISTIC APPROACH TO MODELING OF TIME RANGES

Abstract

The article deals with the use of a hybrid linguistic approach to analysis, modeling and forecasting of time series. For the implementation of the hybrid linguistic approach mathematical formalisms were used: interval mathematics, probability theory, structural (syntactic, linguistic) approach, hidden Markov models (HMM) and formal probability grammars. The hybrid linguistic approach involves the process of constructing linguistic models (LMs) using hidden Markov models (HMM). One of the steps in constructing LM is the use of an interval approach for splitting sets of time series values using elements of interval mathematics and various probability distributions. The morphism of converting numerical images to a symbolic form, which can be used to solve certain problems, is under construction. The proposed methods provide qualitative results in the short-term forecast, which do not differ from the forecasts by profile methods when using less computational resources. During the conduct of numerical experiments, the quality of forecasting of time series of diverse nature at various parameters was proved. Experimental way to find optimal parameters of the algorithm. The algorithm was applied to a variety of time series (social, medical, financial, and economic), calculated static indicators of accuracy of the forecast. Experiments have shown that the algorithm consistently performs the forecast of values in a time series of 3-4 steps ahead and forecasts the trend change by 3-5 steps. The information system with the use of the original mathematical apparatus for analyzing and predicting nonlinear non-stationary processes is developed. Numerical experiments on prediction of time series on different types of intervals (probability distributions). For intervalization, the Beta probability distribution was used; the quality of the time series forecast at various alphabet capacities (number of intervals) was investigated. The tables show the results of the conducted numerical experiments. To estimate the quality of forecasts, the indicator was used based on the Levenstein distance.