COMPLEX VALUED NEURAL NETWORK AND NORMALIZED FOURIER TRANSFORMATION FOR PREDICTION OF TIME SERIES

Time series forecasting is still an open problem in data mining. One major solution that can be used for this problem is Back propagation (BP) neural networks. BPs usually converge to desired final values. But they are usually trained slowly and need large pattern numbers or resources, specially, when the patterns of time series are very complex. In this paper Complex valued neural network (CVNN) is combined with Fourier transformation to improve the prediction accuracy. A CVNN is a neural network that all input, output and weight values are complex numbers. The performance of CVNN is better than traditional feed-forward neural networks. So it can be used instead of them in some real problems to get better accuracy and faster responses. In this paper Fourier transform is applied on times series data to get phase encoded input values. Then left and the most important parts of its respond are used to learn the CVNN. The proposed method in this paper has less neurons number than CVNN. In addition network accuracy is better and it would be adopted faster than CVNN. In addition, three lemmas have been proved which define how to select moving window size and normalization coefficients. The accuracy of the proposed method is compared with four different cases; noisy and noiseless Mackey glass time series, an ecological dataset and two weather datasets.