MFRFNN : Multi-Functional Recurrent Fuzzy Neural Network for Chaotic Time Series Prediction

Chaotic time series prediction, a challenging research topic in dynamic system modeling, has drawn great attention from researchers around the world. In recent years extensive researches have been done on developing chaotic time series prediction methods, and various models have been proposed. Among them, recurrent fuzzy neural networks (RFNNs) have shown significant potential in this area. Most of the proposed RFNNs learn a single function, but when dealing with chaotic time series, different outputs may be generated for a specific input based on the system's state. So, a network is required that can learn multiple functions simultaneously. Based on this concept, a novel multi-functional recurrent fuzzy neural network (MFRFNN) is proposed in this paper. MFRFNN consists of two fuzzy neural networks with Takagi-Sugeno-Kang fuzzy rules, one is used to produce the output, and the other to determine the system's state. There is a feedback loop between these two networks, which makes MFRFNN capable of learning and memorizing historical information of past observations. Employing the states allows the proposed network to learn multiple functions simultaneously. Moreover, a new learning algorithm, which employs the particle swarm optimization algorithm, is developed to train the networks’ weights. The effectiveness of MFRFNN is validated using the Lorenz and Rossler chaotic time series and four real-world datasets, including Box–Jenkins gas furnace, wind speed prediction, Google stock price prediction, and air quality index prediction. Based on the root mean square error, the proposed method shows a decrease of 35.12%,13.95%, and 49.62% from the second best methods in the Lorenz time series, Box–Jenkins gas furnace, and wind speed prediction dataset, respectively

Multi-step-ahead stock price prediction using recurrent fuzzy neural network and variational mode decomposition

Financial time series prediction has attracted considerable interest from scholars, and several approaches have been developed. Among them, decomposition-based methods have achieved promising results. Most decomposition-based methods approximate a single function, which is insufficient for obtaining accurate results. Moreover, most existing research has concentrated on one-step-ahead forecasting that prevents market investors from making the best decisions for the future. This study proposes two novel multi-step-ahead stock price prediction methods based on different decomposition techniques, including discrete cosine transform (DCT), i.e., a linear transform, and variational mode decomposition (VMD), i.e., a non-linear transform. DCT-MFRFNN, a method based on DCT and multi-functional recurrent fuzzy neural network (MFRFNN), uses DCT to reduce fluctuations in the time series and simplify its structure and MFRFNN to predict the stock price. VMD-MFRFNN, an approach based on VMD and MFRFNN, brings together their advantages. VMD-MFRFNN consists of two phases. The input signal is decomposed to several intrinsic mode functions (IMFs) using VMD in the decomposition phase. In the prediction phase, each IMF is given to a separate MFRFNN for prediction, and predicted signals are summed to reconstruct the output. DCT-MFRFNN and VMD-MFRFNN use the particle swarm optimization (PSO) algorithm to train MFRFNN. In this research, for the first time, the gradient descent method is used to train MFRFNN. Three financial time series are used to evaluate the proposed methods. Experimental results indicate that VMD-MFRFNN surpasses other state-of-the-art methods. VMD-MFRFNN, on average, shows a decrease of 31.8% in RMSE compared to the MEMD-LSTM method. Also, DCT-MFRFNN outperforms MFRFNN and DCT-LSTM in all experiments, which reveals the favorable effect of DCT on MFRFNN's performance. To assess the effectiveness of PSO in training VMD-MFRFNN, we compared its performance with twelve different metaheuristic approaches. PSO, on average, shows a decrease of 9.4% in MAPE compared to other metaheuristic methods