About one approach to a volatile time series predicting

Abstract

This article proposes an algorithm of a universe constructing that encompasses historical data of the time series, a fuzzification method of these data using trapezoidal membership functions, and based on them a fuzzy 1st-order model for volatile time series predicting. According to the obtained results, the proposed algorithm for constructing the fuzzy model of the 1st-order provides more accurate value of approximation of the initial time series. Fuzzy sets, as criteria for evaluating historical data values, and fuzzy internal relationships as well (in the form of implicative rules) are divided into groups that reflect cause-effect relationships within the time series and were used to predict it. Based on the application of statistical evaluation criteria MAPE and MSE, it was found that the accuracy of the proposed fuzzy model, taking into account 1st-order internal relationships, is significantly improved using the proposed algorithm of historical data fuzzification. Nevertheless, the model presented in the paper does not pretend to have absolute predicting accuracy, which can be achieved and/or achieved by other more complex higher-order models. The purpose of the article is to show that the use of simple fuzzy prediction models of the 1st-order the opportunity for further improvement of the predicting technology of weakly structured time series. Prediction results of the arbitrary volatile time series demonstrate that the combination of universe establishment algorithms and historical data fuzzification using trapezoidal membership functions, the construction of 1st-order internal cause-effect relationships and the method of defuzzification of outputs of the used fuzzy model can still be superior in quality predicting and prediction reliability not only similar 1st-order models that are presented in the paper, but other models of higher order as well.