Financial time series prediction using hybrids of chaos theory, multi-layer perceptron and multi-objective evolutionary algorithms

Financial Time Series Prediction is a complex and a challenging problem. In this paper, we propose two 3-stage hybrid prediction models wherein Chaos theory is used to construct phase space (Stage-1) followed by invoking Multi-Layer Perceptron (MLP) (Stage-2) and Multi-Objective Particle Swarm Optimization (MOPSO) / elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) (Stage-3) in tandem. In both of these hybrid models, Stage-3 improves the prediction yielded by stage-2. The effectiveness of the proposed models is tested on financial datasets including the exchange rates data of US Dollar (USD) versus Japanese Yen (JPY), British Pound (GBP), Euro (EUR), and Gold price in terms of USD. From the results, it is concluded that Chaos+MLP+NSGA-II hybrid yielded better predictions than the other three-stage hybrid models: Chaos+MLP+MOPSO and Chaos+MLP+PSO, and Two-stage hybrid models: Chaos+PSO, Chaos+MOPSO and Chaos+NSGA-II in terms of both Mean Squared Error (MSE) and Directional Change Statistic (Dstat). Theil's inequality coefficient computed also confirms the superiority of the Chaos+MLP+NSGA-II hybrid over the Chaos+MLP+MOPSO across all datasets. Finally, Diebold-Mariano test indicates that the performance of Chaos+MLP+NSGA-II hybrid is statistically significant than the Chaos+MLP+MOPSO and other hybrids across all datasets. The results of these models are also compared with the two-stage hybrids found in literature [1,2] (Pradeepkumar and Ravi, 2014, 2017). These results are encouraging and suggest further application of these hybrids to other financial and scientific time series prediction problems in the future.