Nonlinear Time Series Analysis Of Chinese Stock Market

According to the efficient market hypothesis (EMH), the prices of assetsin an efficient capital market follow random walk, based on which the modernfinancial analysis system has been established. Contrary to EMH, the fractalmarket hypothesis says that the assets'prices of capital market are followingthe Brownian motion, and have chaotic characteristics. If it is true for thefractal market hypothesis (FMH), then the modern financial analysis systemshould be largely revised. Now, a lot of studies show that chaotic phenomenado exist in capital market. Focusing on the data of Chinese stock market, thispaper uses nonlinear time series analysis methods to study the movement ofstock prices and to test the fractal market hypothesis in Chinese stock market. If the fractal market hypothesis holds true in Chinese stock market, themovement of market prices will show chaotic and fractal properties.Traditional linear time series analysis methods have no use to detect thechaotic and fractal behaviors, but nonlinear ones can do the job. Two kinds oftimes series which are the index series and the index daily return series ofShanghai and Shenzhen stock market are studied in this paper, sample periodsof which spreads from the opening day to September 30th 2003. First of all,qualitative analysis is applied on the series. By the frequency distributionstatistics, differences have been found between market data and the normallydistributed random data. Bispectram analysis, principal content analysis andnear return test further show that there are nonlinearities in the market data,and what's more , via principal content analysis chaos have been found in themarket data. Then, some nonlinear characteristic values of the two kinds of- - IIIseries have been calculated to further confirm the chaotic properties of them.The calculation results show that the correlation dimensions of Shanghai andShenzhen stock index series are 2.131 and 2.4229 respectively; the maximumLyapunov exponents and the Kolmogorov entropies of them all are positivenumbers, which mean that the index series are in chaotic state. The correlationdimension of the Shanghai and Shenzhen index daily return series do notconverge to stable values when increasing the embedding dimension, so theirchaotic properties are not sure. As for a chaotic system, there is strangeattractor in it and the attractor has fractal geometry property, so it is necessaryto study the fractional property of stock data. In this paper, rescaled range(R/S) analysis, detrended fluctuation analysis, and time-increasingmean-variance analysis have been applied to Shanghai and Shenzhen indexdata. These analysis show that the index series have strong long-runpersistence, but their memory term has not been detected and seems notbelong to fractal distributions; as for the index daily return series, they haveclear long-run persistence and the memory term of them are found to be 300and 1090 trading days respectively for Shanghai and Shenzhen's data whichmeans that the index return series are clearly belong to fractal distributions,and they also have significant multifractal properties. In order to reinforce theanalysis, the index data are scrambled and then repeat some of the analysis tothem. The scrambled data never again show the properties of the original dataand behavior more like stochastic time series. From the analysis we get the following results: both index series andindex return series are nonlinear; the index series show strong chaoticbehavior but their fractional properties are not clear; the index daily return- - IVseries show clear fractionalproperties but their chaotic properties are not clear.It can be concluded that the fractal market hypothesis is true in Chinese stockmarket, which contradicts the efficient market hypothesis an...