a theoretical approach to the chaotic time series prediction using mimo anfis

This paper presents an investigation into the use of the time delay coordinate embedding technique with multi-input multi-output adaptive-network-based-fuzzy-inference system (mimo anfis) to learn and predict the continuation of chaotic signals ahead in time. based on the average mutual information and global false nearest neighbors techniques, the optimal values of the embedding dimension and the time delay are selected to construct the trajectory on the phase space. the manfis technique is trained by back propagation algorithm or a hybrid-learning algorithm (a combination of back propagation and the least squares method). first, the parameter set of the membership functions is generated with the embedded phase space vectors using the back-propagation algorithm. second, fine-tuned membership functions that make the prediction error as small as possible are built. the model is tested with the mackey- glass chaotic time series. moving root-mean-square error is used to monitor the error along the prediction and then a phase space for the chaotic time series is reconstructed. forecasting are discussed for the chaotic time series on the reconstructed phase space and on the delay phase space, respectively. the prediction effectiveness of reconstructing a phase space and anfis has been illustrated using commonly used nonlinear, non-stationary and chaotic benchmark datasets of mackey-glass.

A theoretical approach to the Chaotic Time Series Prediction Using MIMO ANFIS

This paper presents an investigation into the use of the time delay coordinate embedding technique with multi-input multi-output adaptive-network-based-fuzzy-inference system (MIMO ANFIS) to learn and predict the continuation of chaotic signals ahead in time. Based on the average mutual information and global false nearest neighbors techniques, the optimal values of the embedding dimension and the time delay are selected to construct the trajectory on the phase space. The MANFIS technique is trained by back propagation algorithm or a hybrid-learning algorithm (a combination of back propagation and the least squares method). First, the parameter set of the membership functions is generated with the embedded phase space vectors using the back-propagation algorithm. Second, fine-tuned membership functions that make the prediction error as small as possible are built. The model is tested with the Mackey- Glass chaotic time series. Moving root-mean-square error is used to monitor the error along the prediction and then a phase space for the chaotic time series is reconstructed. Forecasting are discussed for the chaotic time series on the reconstructed phase space and on the delay phase space, respectively. The prediction effectiveness of Reconstructing a phase space and ANFIS has been illustrated using commonly used nonlinear, non-stationary and chaotic benchmark datasets of Mackey-Glass.