Novel Time Series Analysis and Prediction of Stock Trading Using Fractal Theory and Time-Delayed Neural Networks

Abstract

The stock markets are well known for wide variations in prices over short and long terms. These fluctuations are due to a large number of deals produced by agents and act independently from each other. However. even in the middle of the apparently chaotic world, there are opportunities for making good predictions [1].In this paper the Nikkei stock prices over 1500 days from July to Oct. 2002 are analyzed and predicted using a Hurst exponent (H), a fractal dimension (D), and an autocorrelation coefficient (C). They are H=0.6699 D=2-H =1.3301 and C = 0.26558 over three days. This obtained knowledge is embedded into the structure of our developed time delayed neural network [2]. It is a three layer back propagation type forward neural network with a FIR (Finite Impulse Response) filter of the second order plugged into each input node. It is confirmed that the obtained prediction accuracy is much higher than that by a back propagation-type forward neural network without filters for the short-term.Although this predictor works for the short term, it is embedded into our developed fuzzy neural network [3] to construct multi-blended local nonlinear models. It is applied to general long term prediction whose more accurate prediction is expected than that by the method proposed in [1].