A new ARIMA-based neuro-fuzzy approach and swarm intelligence for time series forecasting

Time series forecasting is an important and widely interesting topic in the research of system modeling. We propose a new computational intelligence approach to the problem of time series forecasting, using a neuro-fuzzy system (NFS) with auto-regressive integrated moving average (ARIMA) models and a novel hybrid learning method. The proposed intelligent system is denoted as the NFS–ARIMA model, which is used as an adaptive nonlinear predictor to the forecasting problem. For the NFS–ARIMA, the focus is on the design of fuzzy If-Then rules, where ARIMA models are embedded in the consequent parts of If-Then rules. For the hybrid learning method, the well-known particle swarm optimization (PSO) algorithm and the recursive least-squares estimator (RLSE) are combined together in a hybrid way so that they can update the free parameters of NFS–ARIMA efficiently. The PSO is used to update the If-part parameters of the proposed predictor, and the RLSE is used to adapt the Then-part parameters. With the hybrid PSO–RLSE learning method, the NFS–ARIMA predictor may converge in fast learning pace with admirable performance. Three examples are used to test the proposed approach for forecasting ability. The results by the proposed approach are compared to other approaches. The performance comparison shows that the proposed approach performs appreciably better than the compared approaches. Through the experimental results, the proposed approach has shown excellent prediction performance.