Random Walk And Criticality Studies In Financial Market Data

Like nature,human society contains strong randomness in some systems and behaviors.The method of statistical physics can help us understanding these phenomena.In recent years,statistical physicists have established a new field of research by using the method of statistical physics.Econophysics is a new interdisciplinary to analyze the financial issues by applying the concept of physics and methods of the physics.Economic and financial system is a large and complex structure and consist of a large number of brokers,the objects of production transaction,rules and so on.With the fast development and profound changes of financial industry in the modern economy and political society activities,coupled with the convenience brought by the Information Internet,broker's learning is easier,Hence,the financial system becomes more complex.Which makes it beyond the ability category of traditional economics in solving problems,so we need to master new research methods and means.The researchers pointed out that the main work direction studying financial physics are the following four aspects:(1)the empirical study on the statistical law of price experience;(2)the study on the stochasticprocess model of price fluctuationthe;(3)the study on the interaction model of brokers in price formation and market evolution;(4)the study on investment portfolio,option pricing and risk control.In this paper,we mainly do some research from(1)and(2).In this paper,we try to make some quantitative description about the random walk characteristics of these complex and variable data by using the Diffusion exponent and the hurst index,and further predict the future volatility on base of these quantizative values.In addition,many complex systems in nature and social sciences show self-organized critical states.In the paper,we examined whether the complex and volatile financial system has the characteristics of self-organized critical.This article includes the following three important parts:(1)The Diffusion exponent has been applied to many fields,even the economic system,as the value of describing the Diffusion of material particles.It can be used to describe the micro fluctuation properties of high frequency index data to a certain extent.In this part,we first make a detailed empirical study on the Diffusion exponent,stock index and stock high frequency data in Chinese stock market.Secondly,we simulate approximately the mechanism of the calculated difference of the different price time series exponent index by using the one-dimensional diffusion model.Finally,we calculate the Diffusion exponent in a short period of time.And we use this quantitative value to predict the future trend of the index price changes and received a good result.This result has a good use value.(2)The Hurst index has always been an important reference for scholars to focus on quantitative indicators of financial market sustainability.This quantitative value is used to measure the sustainability of a period of time.First of all,we study the hurst index about the daily and minute data in China's financial market.and counted the probability distribution of the Hurst index of almost all stock data in the A-share market.The results show that the hurst index in most stock markets are more than 0.50,and the majority of stocks show a continuous cycle for one year.Besides,the results also show that the Hurst index of the day data is generally greater than the minute data.Second,we study the hurst index on the stock index data,and they also have a sustained cycle for one year.But the stock index data showed a significant super-Diffusion property over a short time window(60-120 minutes).Finally,because of some similarities and differences of the Diffusion index and the hurst index in show in quantifying the characteristics for the price time series.We try to explain the causal relationship between these similarities and differences.For example,We find that the calculated value of the Hurst index is generally greater than the calculated value of the difusion index,and The Hurst index reflects a longer duration of sustainability.But for a long time,they all show the normal spread of the stock market that close to the free random walk.We also use the exponential time series's quantization value to predict the future trend,and also have a better effect.(3)The self-organized critical state has been proved to be applied to all fields of nature science,even the social sciences.Howere,for a complex system such as financial market,especially China,a less mature financial markets,whether it is in the self-organized critical state,has always be a common concern for scholars.In this chapter,we prove that China's financial market is also in the self-organized critical state by studying and analyzing the Shanghai Composite Index,the Shanghai and Shenzhen 300 Index and some stock price of time series data.The empirical results also show that A complex financial system in the long term is in the self-organized critical state,but not necessarily in the short term.This may be due to the fact that these phased complex systems are in a different economic and social context.Which leads to the enthusiasm of investors to participate in the transaction,the frequency of transactions,trading psychology,etc.,and thus affect the probability distribution of energy release,so that it is no longer strictly subject to the power law distribution.In summary,our results show that some of the characteristics of the complex and volatile financial system can be quantified with a simple amount.These quantitative values can be used as a reference for investors to invest and even help them make investment decisions,.They may be helpful for the government regulators to conduct quantitative regulation in the market.