Complex Neurofuzzy ARIMA Forecasting—A New Approach Using Complex Fuzzy Sets

A novel complex neurofuzzy autoregressive integrated moving average (ARIMA) computing approach is presented for the problem of time-series forecasting. The proposed approach integrates a complex neurofuzzy system (CNFS) using complex fuzzy sets (CFSs) and ARIMA models to form the proposed computing model, which is called the CNFS-ARIMA. The output of CNFS-ARIMA is complex-valued, of which the real and imaginary parts can be used for two different functional mappings. This is the so-called dual-output property. There is no fuzzy If–Then rule in the genesis of CNFS-ARIMA. For the formation of CNFS-ARIMA, structure learning and parameter learning are involved to self-organize and self-tune the CNFS-ARIMA. A class of CFSs is used to describe the premise parts of fuzzy If–Then rules, whose consequent parts are specified by ARIMA models. CFS is an advanced fuzzy set whose membership degrees are complex-valued within the unit disc of the complex plane. With the synergetic merits of CNFS and ARIMA, CNFS-ARIMA models have excellent nonlinear mapping capability for time-series forecasting. A number of benchmark time series are used to test the proposed approach, whose results are compared with those by other approaches. Moreover, real-world financial time series, such as the National Association of Securities Dealers Automated Quotation (NASDAQ), the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), and the Dow Jones Industrial (DJI) Average Index, are used for the proposed approach to perform the dual-output forecasting experiments. The experimental results indicate that the proposed approach shows excellent performance.