The Fractal Characteristics Of The Stock Market And Stock Prices. Figarch Model Study

This paper analyzed the nonIinear, non--equilibrium, fractaI and chaos characteristicsof Chinese stock market, identified, estimated and tested three fractionalIy integratedtime series modelsThe first chapter "Introduction to the evoIution of stock market investment theory"Summarized the nine important representative theories of different stage, summed up thetrend of the development that the stock market investment theory is evotving from staticportfPlio theory to dynamic time series modeI, from univariate modeI to muItivariate modeI,from linear modeI to nonlinear complicated model and from traditional modeI to fractaImodeI, paved the way for fOllowing discussion.The second chapter "Return, risk of stock market and behavior of stock price"anaIyzed nonlinear and non-equilibrium property of stock market, analyzed the factoresimpact the return and risk of stock market, presented that virtuaI, risk, liquidity andspecuIation are the core character of stock market and stock price shows fractaInonlinear property far from equilibrium, speculation is the premise and nature of stockmarket.The third chapter "Essay of EMH on Chinese stock market" tested the hypothesesfor the EMH on Chinese stock market, presented that stock price and return rate varianceand voIatiIity are not stable. The chapter provided some evidence fOr the non--normaI.non-Gaussian distribution and nonIinear, auto--correlation and Heteroskedasticitycharacter of stock price and return rates, presented that main factors leads to the failureof EMH on Chinese stock market is emotionaI action, information-- based herding,over--reaction and under-reaction to infOrmation of investors and nonIinear,non-equiiibriurn propeFty of stock market.The fourth chapter "Reseach on fractaI structure of stock price" anaIyzed the fractaIstructure of stock price, deduced the investment function, caIculated the Hurst Exponent,3correlation dimension, and max Lyaponov Exponent, analyzed the self-similarity, long range dependence, circulation period of stock price and sensitivity of stock price to the initial value, suggested took the exponent characterize fractal instead of variance as instrument to measure risk.The fifth chapter "Stock price ARFIMA, GARCH and FIGARCH model" introduced different kinds of time series models including fractal model, method such as analysis of variance(ANOVA) and unit root test to test the stability of time series, method and criteria to estimate the ARFIMA, GARCH and FIGARCH model. The paper tested the stability of Shanghai Stock Exchange Comprehensive Index and logarithm return rates of which.The sixth chapter "Essay on the estimation of stock price model" briefly introduced evolution of Chinese stock market, showed the abrupt change and discontinuity of Chinese stock market return, estimated the three models on the Shanghai Security Exchange comprehensive Index, compared the result made by the three models?The result showed that the FIGARCH model is better in modelling the autocorrelation, Heteroskedasticity and nonlinear characteristics of stock price than the others.