On Some Models for Value-At-Risk
扩展了条件自回归风险价值（CAViaR）模型，提出阈值GARCH和混合GARCH两种新模型来捕捉风险价值的非线性和结构变化，并应用于多个股票指数。
The idea of statistical learning can be applied in financial risk management. In recent years, value-at-risk (VaR) has become the standard tool for market risk measurement and management. For better VaR estimation, Engle and Manganelli (2004 Engle , R. , Manganelli , S. ( 2004 ). CAViaR: Conditional value at risk by regression quantiles . Journal of Business & Economic Statistics 22 : 367 – 381 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) introduced the conditional autoregressive value-at-risk (CAViaR) model to estimate the VaR directly by quantile regression. To entertain the nonlinearity and structural change in the VaR, we extend the CAViaR idea using two approaches: the threshold GARCH (TGARCH) and the mixture-GARCH models. The estimation method of these models are proposed. Our models should possess all the advantages of the CAViaR model and enhance the nonlinear structure. The methods are applied to the S&P500, Hang Seng, Nikkei and Nasdaq indices to illustrate our models.