An Empirical Analysis Of Chinese Stock Market Crash Critical Time Based On Log-periodic Power Law

The traditional efficient market theory assumes that everyone in the market is a rational economics man. The stock price reflects the balance between supply and demand of these rational man, and also fully reflects all available information about the asset. The competition in the market will make the stock price transform to a new equilibrium from the old equilibrium eventually, and the change of the price that under the new information is independent for each other or random, eventually the market is efficient, the balance is the normal state of the market. And at present, the practice in most countries stock market in the world proved that the distribution of the stock earnings rate is sharp peak and long-team memory, the traditional efficient market theory is not appropriate obviously. Under the non-linear analysis thought, scholars put forward the fractal market theory which is corresponding with the efficient market theory, and the transmission of information is not evenly spread because different investors has different judgment about the same information. The price does not reflect the information that people has got at any point, it only simply reflects the importance of the information that corresponding with the time limation of the investment. The response to market information is not the traditional assumption of a simple linear relationship, there is a positive feedback and self-similar characteristics in the market, the earnings rate has a long-term memory effects, volatility of the market is not completely disordered, and the price sequence follows the biased Brown movement, so there are a large number of non-equilibrium in the market.To analyze the earnings rate of China’s stock market, we can get the distribution is sharp peak and fat tail, it means that China’s stock market is non-linear, and then we can obtain the hurst index through the R/S analysis method, if it is more than0.5we can know the China’s stock market is fractal. The stock market has fractal characteristics and earning rate is a power-law distribution, the main reason is that the positive feedback existence in the market, and the herd behavior that caused by positive feedback also make the market bubbles. It means the market is failure, if so, we can’t learn the operation of the market, and the operation of the market bubble also has it’s own rule. Positive feedback lead to bubble growth, from the perspective of physics, it belongs to the self-organized state is an attraction domain, even though we changed the initial conditions, system will reach the critical state eventually.In the critical state, the relationship between the size of the events in the system and its frequency is power function, then the characteristic scale of the system does not exist, but we can make some description based on fractal theory invariance principle of the market. In the stock market, mutual influence between heterogeneous investors until the last consistent behavior, and it leads to a bursting of the bubble, which is the stock market’s self-organized criticality. There are two features in Log-periodic power law model, one is logarithmic oscillates in a period, the second is the power-law growth or decay. Accelerated rise in the stock market is a bubble process in line with these two features, so we can use the log-periodic power law model fitting bubble evolution process, and identify the critical time that bubble burst.Firstly, to identify the presence of the stock market since the organization of the state according to the market trends in the duration, this state is the accumulation of foam to maturity from one end to the rupture cycle. Then use the log-periodic power law model to fit on the bubble, then can identify the critical time that bubble burst. Through the empirical study of the Chinese stock market we found that the Shanghai Composite Index, Shenzhen Component Index, the GEM and stock prices, can use the log-periodic power law model to fit well, and get fit critical time in bubble burst in real time within the error range. After it, LPPL model is analyzed robustly in this article, the results is in different periods the critical time error within the acceptable range, the data is longer, the closer to collapse time, and the results of critical time that fit the LPPL model is relatively more accurate. These features appear in the stock market allows us to act for investors, and the operation of the stock market and other aspects of the internal mechanism to analysis more detail in different angles, which not only allows us to understand the market more accurately, but also provide some reference for policy makers when they develop policies. Finally, give three policy recommendations to China’s stock market bubble:first to maintain the stability of macroeconomic policies, to prevent significant changes in the policy itself caused the stock market bubble. The second should strive to create an open and transparent market environment, reduce the stock market bubble that caused by information asymmetry. Third, we must develop sophisticated institutional investors, they can become the backbone to stabilize the market, and also to strengthen the ordinary investor education, and training rational investment philosophy.