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  • Carlos Martins-Filho (a1) (a2), Feng Yao (a3) (a4) and Maximo Torero (a2)


We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous variables, are assumed to be strong mixing and follow a nonparametric conditional location-scale model. First stage nonparametric estimators for location and scale are combined with a generalized Pareto approximation for distribution tails proposed by Pickands (1975, Annals of Statistics 3, 119–131) to give final estimators for CVaR and CES. We provide consistency and asymptotic normality of the proposed estimators under suitable normalization. We also present the results of a Monte Carlo study that sheds light on their finite sample performance. Empirical viability of the model and estimators is investigated through a backtesting exercise using returns on future contracts for five agricultural commodities.


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*Address correspondence to Carlos Martins-Filho, Department of Economics, University of Colorado, Boulder, CO 80309-0256, USA; and IFPRI, 2033 K Street NW, Washington, DC 20006-1002, USA; e-mail:,


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We thank Peter C. B. Phillips, Eric Renault, an Associate Editor and an anonymous referee for comments that improved the paper substantially. Any remaining errors are the authors’ responsibility.



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  • Carlos Martins-Filho (a1) (a2), Feng Yao (a3) (a4) and Maximo Torero (a2)


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