Multi-Step Ahead Prediction Of Chaotic Time Series Using Recurrent Neural Network Models
Sanjay L. Badjate, Sanjay M. Gulhane · 2011
In this paper the multi step ahead prediction of typical Duffing Chaotic time series and the monthly sunspots real time series are carried out. These two time series are popularized due to their highly chaotic behavior. This paper compares the performance of two neural network configurations namely a Multilayer Perceptron (MLP) and proposed FTLRNN with gamma memory for the duffing time series for 1, 5,10,20,50 and 100-step ahead prediction and for monthly sunspot time series for 1, 6, 12, 18 & 24 month ahead prediction . The standard back propagation algorithm with momentum term has been used for both the models. It is seen that estimated dynamic fully recurrent model clearly outperforms the MLP NN in various performance matrices such as Mean square error (MSE), Normalized mean square error (NMSE) and correlation coefficient ( r) on testing as well as training data set for multi step prediction (K=1,5,10,20,50,100) for duffing time series and for the sunspot time series for 1, 6, 12, 18 &24 month ahead prediction. In addition, the output of proposed neural network model closely follows the desired output for all the step ahead prediction. It is observed that suggested recurrent models have the remarkable capability of time series prediction. The major contribution of this paper is that Various parameters like number of processing elements, step size, momentum value in hidden layer, in output layer the various transfer functions like tanh, sigmoid, linear-tan-h and linear sigmoid, different error norms L1, L2 ,Lp to L.