Statistical Inference for a Relative Risk Measure

ABSTRACT

For monitoring systemic risk from regulators’ point of view, this article proposes a relative risk measure, which is sensitive to the market comovement. The asymptotic normality of a nonparametric estimator and its smoothed version is established when the observations are independent. To effectively construct an interval without complicated asymptotic variance estimation, a jackknife empirical likelihood inference procedure based on the smoothed nonparametric estimation is provided with a Wilks type of result in case of independent observations. When data follow from AR-GARCH models, the relative risk measure with respect to the errors becomes useful and so we propose a corresponding nonparametric estimator. A simulation study and real-life data analysis show that the proposed relative risk measure is useful in monitoring systemic risk.

KEY WORDS:

• Copula
• Expected shortfall
• Jackknife empirical likelihood
• Nonparametric estimation
• Systemic risk.

Acknowledgments

We thank the editor, Professor Todd Clark, an associate editor, and two reviewers for their helpful comments. Peng’s research was partly supported by the Simons Foundation. Sheng’s research was partly supported by the National Natural Science Foundation of China (nos. 71161013 and 71561011) and the Science and Technology Project of Jiangxi Provincial Education Department (no. GJJ14323).