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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. 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. It is confirmed that the obtained prediction accuracy is much higher than that by a back propagation-type forward neural network for the short-term. Although this predictor works for the short term, it is embedded into our developed fuzzy neural network 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.