Parameter Estimation And Application Of Autoregressive Conditional Heteroscedasticity Model

Nonlinear autoregressive conditional heteroskedasticity model (ARCH) is mainly toadopt the variance regression to describe the dynamic features about random concussioninformation in economic time series. Because the variance of the time series wobbles asthe change of time is a main dynamic characteristics of financial time series. Through theanalysis of the corresponding model, we can further know the structure character and thechange law of data, so we can achieve the purpose of forecasting its development trendand putting up essential control.The paper mainly studied the optimization method of the parameter estimate and itsapplication in ARCH model. And according to the heteroscedasticity of time series give itsfurther carefully analysis, research and predict.Firstly, used the optimization algorithm methods of grey model GM(2,1) as the mainline, and by using least square method to improve GM(2,1) algorithm and get itsprediction steps by MATLAB, for the observation time series fitting out the mathematicalmodel. For non-stationary time series model is decomposed into random and deterministicpart, combined with auto-regressive conditional heteroskedasticity model ARCH(q) forresidual extraction doing further research. We use NLBFGS optimization algorithm toestimate its parameters, and given its proof of convergence. It verified the applicabilityand practicability of the ARCH model indirectly.Secondly, constructed the N-ECM algorithm of nonlinear time series, and based onN-ECM algorithm to solve parameters under the censored data, the article gave analgorithm of logarithmic normal distribution under the random censored data. We knowthat ARCH model can be approximated as normally distributed. Parameter estimationusing logarithm likelihood estimate Algorithm in ARCH model we will get its iterativeformula. Finally, there will give examples using MATLAB to further explain theapplication of N-ECM algorithm in financial time series.Finally, constructed a new algorithm of nonlinear time series, and based on theSAA-LM algorithm which combined with Simulate Anneal Arithmetic and Levenberg-Marquardt, and was used to the parameter estimation of the ARCH model. Itsprediction effect was obvious. Make a comparison, the results show that the newalgorithm is better.