Multi step ahead prediction of north and south hemisphere sun spots chaotic time series using focused time lagged recurrent neural network model

• Authors: Sanjay L. Badjate;Sanjay V. Dudul
• Venue: WSEAS Transactions on Information Science and Applications
• Year: 2009

Multi-Step ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multistep ahead prediction of North and South hemisphere sunspots chaotic time series. In the literature there is a wide range of different approaches but their success depends on the predicting performance of the individual methods. Also the most popular neural models are based on the statistical and traditional feed forward neural networks. But it is seen that this kind of neural model may present some disadvantages when long-term prediction is required. In this paper focused time lagged recurrent neural network (FTLRNN) model with gamma memory is developed not only for short-term but also for long-term prediction which allows to obtain better predictions of northern and southern chaotic time series in future. The authors experimented the performance of this FTLRNN model on predicting the dynamic behavior of typical northern and southern sunspots chaotic time series. Static MLP model is also attempted and compared against the proposed model on the performance measures like mean squared error (MSE), Normalized mean squared error (NMSE) and Correlation Coefficient (r). The standard back propagation algorithm with momentum term has been used for both the models. The various parameters like number of hidden layers, number of processing elements in the hidden layer, step size, the different learning rules, the various transfer functions like tanh, sigmoid, linear-tanh and linear sigmoid, different error norms L1, L2 (Euclidean), L3, L4, L5 and L∞, and different combination of training and testing samples are exhaustively varied and experimented for obtaining the optimal values of performance measures. The obtained results indicates the superior performance of estimated dynamic FTLRNN based model with gamma memory over the static MLP NN in various performance metrics. In addition, the output of proposed FTLRNN neural network model with gamma memory closely follows the desired output for multi- step ahead prediction for all the chaotic time series considered in the study.