Analysis Of Fluctuations Of Shanghai Comprising Index Based On Fractal Theory

Starting from the modern financial frontier-complex system we looked back basicapproaches and principles of the chaos, fractal theory and Fractal Market Hypothesis. Weshowed that the chaos and fractal theory could reflect the essence of the financial marketas complex system. Based on Fractal Market Hypothesis, we studied the behaviors of thestock market in the methods of fractal theory that was one branch of complex system. Ourdiscussion focused on the characteristics of fractal system: long-term correlation andstatistical similarity. We showed that the two properties were consistent as intrinsicproperty 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 HurstExponents estimated were stably more than 0.5 in all time scales, and it meant that therewas long-term persistence in Chinese stock market, namely the behaviors of the stockmarket followed the skew random walk model. In R/S analysis we found the evidence of"Non-periodic Cycle" in stock market with average cycle of 315 days. In the terms offractal statistics, fractal market also existed. After the changes of time scales the scattersand the probability distributions also remained the similar shapes, while this showed therewere the structures of similarity in the stock market. In summary, the empirical resultsdemonstrated that the stock market was of intrinsic property of chaos and fractal system.