Study On Financial Market Based On Multi-fractal And Chaotic Theories

Although based on the efficient market hypothesis (EMH), the modern financial analysis system is not"efficient"enough to study the financial market. With the rapid development of the nonlinear science, the fractal theory and chaotic theory have been widely used in dealing with the movement of the market prices. But as an important index to describe the dynamics of the financial market, the trade volume has been given little attention, because of which the accurate, clear and comprehensive description of the financial market dynamics has not been accomplished.The movement of market prices and trade volume of many kinds of the financial markets, such as Shanghai stock market, Nasdaq stock market, New York oil futures, London copper futures, USD/JPY exchange rate and USD/AUD exchange rate, has been comprehensively studied by some nonlinear methods. Especially, the trade volume is firstly studied and the financial market risk- evaluated method based on multi-fractal theory has been firstly proposed by this paper.First, the result of R/S analysis shows that the movement of market prices and trade volume of every kind of the financial markets has obvious nonperiodic circle, with Hurst index large than 0.5 and C (t) large than 0, which indicates clear fractal properties. And the result also shows that the influence of price limit on the fractal properties of Shanghai stock market is very remarkable.Second, the space projection result shows that the close price daily series of Shanghai stock market and New York oil futures have obvious chaotic property while the close price daily returns series not, for which the chaotic characteristic values are calculated by the close price daily series in this paper.The autocorrelation function method, C-C method and G-P method has been used to determine the delay time and the embedding dimensions in studying on Shanghai stock market and New York oil futures, but the result shows that the delay time and the embedding dimensions gotten from different methods were different, C-C method being worst robust. Further more, the positive maximum Lyapunov exponents and the non-integer correlation dimensions of market prices series of Shanghai stock market and New York oil futures show obvious chaotic properties, but the positive maximum Lyapunov exponents and the small correlation dimensions of the trade volume series of Shanghai stock market and New York oil futures show unconspicuous chaotic properties, which accords with the result of the space projection.Third, in order to investigate the fractal properties of the financial market comprehensively, the multi-fractal detrended fluctuation analysis (MF-DFA) and the box dimension multi-fractal spectrum method have been used in studying on themovement of market prices and trade volume of the financial markets, from which the correlation between h(q) and q and the H?lder indexαvarying between large scales has been found, showing obvious multi-fractal properties with different cause of formation .In conclusion, the movement of market prices and trade volume of every kind of the financial markets has obvious multi-fractal properties and chaotic properties, showing obvious multi-fractal and chaotic dynamics, for which the linear efficient market hypothesis (EMH) can not be adapted to dealing with the nonlinear phenomenon of the financial markets.Finally, the indicator for evaluating the risk of the financial markets based on multi-fractal theory has been firstly proposed by this paper. Comparing with the financial market risk- evaluated method based on Hurst index proposed by Peters, the multi-fractal method in this paper is more effective than Peters's method.