The Bayesian Statistical Analysis Of GARCH-GED Model

General error distribution(GED) is a typical heavy tail distribution, and thickness of its tail can be adjusted by the value of its shape parameter p . In particular, when p = 2, this distribution is known as normal distribution. It was first introduced in 1920s, and then Vianelli presented the standard form of density function in 1960s. Since then, many scholars did lots of researches on its parameter estimation, generation method of random number, etc. In this paper the author mainly discusses the Bayesian parameter estimation using MCMC Method, constructs the GERCH-GED Model based on GED distribution, and then gives the Bayesian analysis and data verification through simulation.Theoretical background and practical significance of Bayesian parameter estimation of GARCH model based on GED Distribution is discussed for the first time in this paper. The basic characteristics of financial time series, the found of GARCH Model and the reason replacing normal assumption of return rate distribution with GED Distribution in GARCH Model that describes the behavior of stock prices are discussed. Also the definition, characteristics of GED Distribution and conclusions such as the existing parameter estimation method as well as sampling methods are presented.Gibbs sampling method is used to construct Markov Chain during the discussion of Bayesian Estimation of GED Distribution parameters with MCMC Method. When dealing with sampling issue of complicated non-log-concave posterior density, ARMS sampling which adds a Metropolis-Hastings step in the process of ARS, is introduced, hence sampling efficiency was improved. GARCH-GED Model is constructed in the last section of this paper, and detailed analysis of parameter estimation with Bayesian Method is discussed.In the last two chapters Bayesian estimation for both the GED Distribution and GARCH model parameters is discussed. Simulated data are used to verify the effectiveness of the estimation. After conducting the data estimation of practical return rate, the author found that fitting GED distribution to the heavy-tailed return rates for stock prices is reasonably good.