Forecasting in non-stationary environments with fuzzy time series

Abstract

Time series arise in many fields of science such as engineering, economy and agriculture to cite a few. In the early 1990’s the so called Fuzzy Time Series were proposed to handle vague and imprecise knowledge in time series data and have since become competitive forecasting models. A common limitation of recent fuzzy time series models is their inability to handle non-stationary data. Thus, in this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS). In the proposed method, we employ Non-Stationary Fuzzy Sets, in which perturbation functions are used to adapt the membership function parameters in the knowledge base in response to statistical changes in the time series. The flexibility of the method by means of computational experiments was tested with eight synthetic non-stationary time series data with several kinds of concept drifts, four real market indices (Dow Jones, NASDAQ, SP500 and TAIEX), three real FOREX pairs (EUR-USD, EUR-GBP, GBP-USD), and two real cryptocoins exchange rates (Bitcoin-USD and Ethereum-USD). As competitor models the Time Variant fuzzy time series and the Incremental Ensemble were used, these are two of the major approaches for handling non-stationary data sets. The proposed method shows resilience to concept drift, by adapting parameters of the model, while preserving the symbolic structure of the knowledge base.