The Application Of Statistic Physics To Properties Of Chinese Stock Market

Since 1980s, people have found that some basic hypotheses on which financial theories rely do not accord with the empirical results. If we want to revise them or establish new theory, we should first analyse comprehensively the peoperties of financial market. Stock market is a complicated multi-body system and so the price fluctuations are the results of interactions of multi-bodies. Statistical physics is the subject that studies the results and fundamental principles of interactions of multi-bodies. According to the closing stock index of different time scales in Shanghai and Shenzhen and with the help of the theories and methods of statistical physics, this dissertation makes a thorough and systematic study on the properties of Chinese stock market and provides empirical results for dynamic mechanism of price fluctuations. It is made of five parts.The first is the scaling properties. By using the Rescaled Range Analysis and the Detrended Fluctuation Analysis, we study the scaling properties of return series and find there is long-range memory. The Hurst exponents are 0.6282 and 0.6358 respectively in Shanghai stock market and Shenzhen stock market. We also find there are 284-day long memory period and 115-day short memory period. The persistence becomes weak when scale shortening, but it becomes strong when time range shortening. The fluctuation becomes complicated when the scale becomes short. As to the absolute value series and square value series of returns, there are stronger long-range persistence.The second is the properties of returns. According to the high-frequency closing stock index, we study the probability distributions of returns and find the middle part of the distribution is well described by the Lévy stable distribution with Lévy Exponents 1.26 in Shanghai and 1.74 in Shenzhen. The asymptotic behaviour of the distribution is truncated Lévy distribution.The third is the volatility. We analyse the statistical properties of volatility in Shanghai stock market and find there are scale invariance both in probability distribution and cumulative probability distribution. The former can be well described by a log-normal function and there are power law and crossover time, which is about four days. The Shanghai stock market has obvious day-effect whick shape is like the word"W".The forth is the multifractal. We put forward three methods of multifractal and have conclusions that Shanghai stock market has weak multifractal and its shape does not change with scales, but its strength weakens with the scale shortening. The general Hurst exponent decreases when the order of partition function increases. The shorter the scale, the stronger it decreases. The singular spectrum function does not change continuously with partition order. It is like the behaviour of the order parameter at its critical point.The last one is the order parameter of stock market. With analogy, we believe the general dimension D q or the general Hurst exponent h (q) as the order parameter, the important parameter in phase transition and analyse its properties.