Analysis Of Fluctuations Of Chinese Future Market Based On Chaos And Fractal Theory

Starting from the modern financial frontier-complex system we looked back basic approaches and principles of the chaos, fractal theory and Fractal Market Hypothesis. We showed that the chaos and fractal theory could reflect the essence of the financial market as complex system. Based on Fractal Market Hypothesis, we studied the behaviors of the future market in the methods of fractal theory that was one branch of complex system. Our discussion focused on the characteristics of fractal system: long-term correlation and statistical similarity. We showed that the two properties were consistent as intrinsic property of complex system. In the empirical analysis, we found strong evidence of long-term persistence and statistical similarity on Chinese future market. Using R/S analysis, we estimated Hurst Exponent to characterize the long-term persistence. The Hurst Exponents estimated were stably more than 0.5 in all time scales, and it meant that there was long-term persistence in Chinese future market, namely the behaviors of the future market followed the skew random walk model. In R/S analysis we found the evidence of "Non-periodic Cycle" in future market with average cycle between 75 days and 80 days. In the terms of fractal statistics, fractal market also existed. After the changes of time scales the scatters and the probability distributions also remained the similar shapes, while this showed there were the structures of similarity in the future market. Also by analyzing the Lyapunov exponents of future prices series, we estimated the predicted time as long as possible with the longest some 78 days. And it showed that the empirical results of chaos and fractal theory were consistent in the error scale. In summary, the empirical results demonstrated that the future market was of intrinsic property of chaos and fractal system. We further conducted Elliott Wave analysis of the chaotic prediction and applied the average cycle to the prediction. The empirical results of Elliott Wave theory put forward a further proof of the existent of the fractal structure.