The Quantile Estimation For Power-ARCH Model

Quantile estimation, introduced by Koenker&Bassett(1978), it is an extension for the least square estimation based on the classical conditional mean model. Quantile estimation through calculating the minimum of sum of weighted residuals of absolute value to estimate the parameter values, it stress to get the quantile estimation of the explanatory variable in turn to obtain the quantile estimation of the dependent variable, bulid the quantile estimation equation, and use the method of linear programming and nonparametric estimation method to estimate the corresponding to different quantile explanation variable coefficient or unknown parametersso. This can also be referred to as "weighted least squares estimate". LAD estimation is only a special quantile estimation.This paper mainly studied the quantile estimation of the Power-ARCH(1) model, and the parameter estimation of the strong consistency and the asymptotic normality. the main content is as follows:1, The paper first introduces the basic knowledge of the quantile estimation and GARCH class models.2, The paper also simply introduced the basic knowledge of random variables and time series, and detailed introduced the idea of the quantile estimation and the strong consistency and asymptotic normality for the quantile estimation of the linear model.3, The paper mainly introduced the quantile estimation of the Power-ARCH(1) model, and proved the strong consistency and asymptotic normality of the estimation.4, The paper also made the corresponding empirical analysis by the the Matlab、 R and Eviews, and also gived the reasonable.