Real valued Time Series Prediction by Complex Valued Neural Network and Normalized Fourier Transformed Data

Time series forecasting is still an open problem in data mining. One major method that is dealing for this problem is Back propagation (BP) neural networks. BPs are very stable and usually converge to a final state. 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 suggested. A CVNN is a neural network that all input, output and weight values are complex numbers. The functionality of CVNN is higher than traditional feed-forward neural networks. So it can be used instead of them in some real problems to get better or 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 efficiency is better and it would be adopted faster than CVNN. In addition, three lemmas have been proved which define how to select ongoing window size and normalization coefficients. At last, the advantage of the proposed method is compared as three different cases; noisy and noiseless Mackey glass time series, an ecological dataset and a weather dataset