An Investigation into the Use of Delay Coordinate Embedding Technique with MIMO ANFIS for Nonlinear Prediction of Chaotic Signals

This paper presents an investigation into the use of the delay coordinate embedding technique with multi-input multi-output (MIMO) adaptive-network-based-fuzzy-inference system (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 gradient descent algorithm. 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 both periodic and the Mackey-Glass chaotic time series. Moving root-mean-square error is used to monitor the error along the prediction horizon.