| Volatility is an important attribute of the securities market, is the important issues facedby the Quantitative Economics and Statistical Science, and is closely related to the functionof financial market stability, It is at the heart of financial asset pricing and asset allocationand it is an effective indicator of market price behavior, quality and efficiency. To adeveloping mature capital markets, there should be a moderate, stable fluctuate slightly, butthe frequent and volatility big shock, is not only bad for investment participants making theright portfolio strategy, but also endanger the financial health rapid and stable developmentof the market, and even induce global financial crisis. More and more scholars areconcerned on the fluctuations of the securities market characteristics and influencing factors.China launched the Shanghai and Shenzhen300stock index futures in2010, stock marketvolatility has become more complex. This article starts to research the Shanghai andShenzhen300stock index in this context, for the research methods as the autocorrelationand heteroscedasticity of the stock index sequence we can no longer apply the traditionalsense of the rate of return and risk metrics, so ADF (Unit Root Test) cointegration test arerequired. At last we establish an EGARCH model reflects the asymmetry of the stockmarket.This paper describes the basic theory of the ARCH model to analyze the characteristicsof the nature of these models, and focus on the model parameter estimation method. Themost widely used estimation method is maximum likelihood estimation method. Althoughsome scholars have proposed some of the more advanced algorithms such as BHHHalgorithm and Generalized Method of Moments (GMM) to get the distribution of the modelparameters and thus to obtain more information in the model parameters. However, in theactual operation of such an algorithm is often encountered intermediate data shock resultingalgorithm overall failure. Some academics have also chosen to use a Markov chain MonteCarlo (MCMC) methods to calculate the posterior distribution of GARCH Models. Thismethod, however, need to take some difficult sampling metheds such as Griddy-Gibbs,Metropolis-Hastings sampling method. Domestic scholars raised a simple and effectiveconventional Monte Carlo method to estimate GARCH (1,1) model parameters, on the basisof the work we choose the Halton sequence of alternative uniformly distributed in theoriginal method as a parameter of the prior distribution, and the method is extended to theEGARCH model from the GARCH (1,1) model. Eventually the result showed that it iseffective of this method when estimating the EGARCH model parameters.In this paper, from the following aspects:1) Systematically expound the background the statistical significance and domesticand foreign research status development level of the regression model ofautoregressive conditional heteroskedasticity. detailed descript the Bayesianinference theory which is the basis of the Monte Carlo method used in the article.2) Elaborately elaborate the theoretical part of the Monte Carlo method, usingMATLAB software design experiments, the comparative analysis the quasi-random number and the difference between the pseudo-random number,intuitive experimental results presented in this article using the quasi-randomnumbers instead of the pseudo-random better statistical properties for severalreasons-quasi-random number.3) Combine with the China’s stock market, through the analysis of time-series dataon the CSI300Index in the empirical analysis, we establish EGARCH model,give the Monte Carlo estimation method. By the comparison with the result ofmaximum likelihood estimation method we prove the effectiveness of thismethod. |
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