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In this article, by using composite asymmetric least squares (CALS) andempirical likelihood, we propose a two-step procedure to estimate theconditional value at risk (VaR) and conditional expected shortfall (ES) for theGARCH series. First, we perform asymmetric least square regressions at severalsignificance levels to model the volatility structure and separate it from theinnovation process in the GARCH model. Note that expectile can serve as a bondto make up the gap from VaR estimation to ES estimation because there exists abijective mapping from expectiles to specific quantile, and ES can be inducedby expectile through a simple formula. Then, we introduce the empiricallikelihood method to determine the relation above; this method is data-drivenand distribution-free. Theoretical studies guarantee the asymptotic properties,such as consistency and the asymptotic normal distribution of the estimatorobtained by our proposed method. A Monte Carlo experiment and an empiricalapplication are conducted to evaluate the performance of the proposed method.The results indicate that our proposed estimation method is competitive withsome alternative existing tail-related risk estimation methods.

Conditional Tail-Related Risk Estimation Using Composite Asymmetric Least Squares and Empirical Likelihood