Heteroskedasticity Model Modeling Research

In time series modeling, we often encounter the problem that Heteroscedasticity return error variance depends on the extent of the changes in the past error, and change over time, thus demonstrating fluctuations in the grouping. The traditional model used in the analysis, linear regression model, ARMA model, adopted zero expectations, and subject to independent variance with the assumption that no objective and accurate description of the variance changes in the colonization and variability. And since the handover conditional heteroskedasticity (ARCH) model (from Robert Engle (1982) first proposed) because of a good statistical properties of volatility and accurate description applicable to the types of time series data on the economy, such as stock prices, interest rates, foreign exchange rate and so on regression analysis and forecasting.But in the application of economic and financial fields,a large number of practical problems, the nonlinear time series residual often showed two peaks and more peaks, then a single heteroscedasticity difficult to provide accurate forecasting results were mixed model provides a distribution can be approximated by any form of flexible and effective way.Heteroscedasticity on the model parameter estimation using Bayesian parameter estimation, simulation, the maximum likelihood estimation method than the classical better. For the hybrid model parameter estimation using classical methods is difficult to estimate ,the paper is to simplify the method by adding mixed data distribution, together with the Bayesian parameter estimation method and the EM algorithm for the estimation, thereby improving the operability of the estimate, the effective parameters to be estimated.This work is on the one hand for a single peak of the Heteroscedasticity ARCH model parameters using Bayesian estimation, Gibbs sampling algorithm combined with simplified simulation algorithm.ARCH models in the light of the other modeling the actual lack of a detailed discussion of the mixed GARCH modeling and application of simulation and the actual data, the hybrid model are found to have no more than a single model Heteroscedasticity better results.The significance of this paper is, first, to discuss the current nonlinear time series model, and in light of the lack of actual data fitting, nonlinear mixed-time series model. Second, the use of Bayesian parameter estimation and Gibbs sampling algorithm to improve the traditional parameter estimation.