Intelligent financial time series forecasting: A complex neuro-fuzzy approachwith multi-swarm intelligence

Financial investors often face an urgent need to predict the future. Accurate forecasting may allow investors to be aware of changes in financial markets in the future, so that they can reduce the risk of investment. In this paper, we present an intelligent computing paradigm, called the Complex Neuro-Fuzzy System (CNFS), applied to the problem of financial time series forecasting. The CNFS is an adaptive system, which is designed using Complex Fuzzy Sets (CFSs) whose membership functions are complex-valued and characterized within the unit disc of the complex plane. The application of CFSs to the CNFS can augment the adaptive capability of nonlinear functional mapping, which is valuable for nonlinear forecasting. Moreover, to optimize the CNFS for accurate forecasting, we devised a new hybrid learning method, called the HMSPSO-RLSE, which integrates in a hybrid way the so-called Hierarchical Multi-Swarm PSO (HMSPSO) and the wellknown Recursive Least Squares Estimator (RLSE). Three examples of financial time series are used to test the proposed approach, whose experimental results outperform those of other methods.