Fractal Characteristics Of Chinese Stock Returns And Chaos

Based on the fractal theory and the basic concepts of chaos, we find some conclusions as follows through taking an empirical research on daily, weekly and monthly gain rates of the Shanghai stock index and Shenzhen stock index from 1990 to 2006 by applying the Rescaled range (R/S) analysis.(1) As for Shanghai stock index (Shenzhen stock index): The average circles of the daily gain rate, weekly gain rate and monthly gain rate are 272 exchange days,52 exchange weeks and 36 exchange months(324 exchange days,64exchange weeks and 42 exchange months),respectively. Accordingly, the Hurst exponents are 0.6116, 0.6488, 0.6342 (0.616, 0.6586, 0.6982); the fractal dimensions of time series are 1.3884, 1.3512, 1.3658(1.384, 1.3414, 1.3018); the fractal dimensions of probability space are 1.635,1.5413,1.5768 (1.6233,1.5184,1.4323), respectively.The above datum show the grain rates of Shanghai stock index and Shenzhen stock index fall short of normal distribution obviously ,are self correlative, own fractal characteristic and nonlinear dynamics behavior.(2) By calculating the daily grain rates of Shanghai stock index and Shenzhen stock index, the correlation dimensions of Shanghai stock index and Shenzhen stock index are 2.89 and 3.06.The analysis shows our stock market is complicate and there are a lot of factors determine the operation of market, but only two or three factors are of the essence.(3) By reconstructing the phase space, we find the existence of chaos attractor, meanwhile, by using of the software Matlab6.5 and Eviews3.1, we take a prediction on the grain rates of Shanghai stock index and Shenzhen stock index, the precision reaches more than 97%.