Nonparametric estimation of conditional VaR and expected shortfall

作者：Cai, Zongwu^*; Wang, Xian

来源：Journal of Econometrics, 2008, 147(1): 120-130.

DOI：10.1016/j.jeconom.2008.09.005

• Boundary effects
• Empirical likelihood
• Expected shortfall
• Local linear estimation
• Nonparametric smoothing
• Value-at-risk
• Weighted double kernel

This paper considers a new nonparametric estimation of conditional Value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya-Watson estimators, Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical Study is carried out to illustrate the finite sample performance of the proposed estimators. Published by Elsevier B.V.

• 出版日期2008-11
• 单位厦门大学