A New Estimator for Conditional Expectile-Based Value-at-Risk of a Linear Predictive Regression

Since it is the only elicitable law-invariant coherent risk measure, the expectile-based value-at-risk (EVaR) is a recently recommended risk measure in financial risk management. This paper considers the large sample statistical inference problem of conditional EVaR under a linear predictive regression model. Based on the least-squares residuals, we propose a novel least-squares residual estimator for the conditional EVaR of a linear predictive regression. The asymptotic properties of the proposed estimator are investigated in the context of dependence. We illustrate that the proposed estimator is computationally efficient and has desirable finite sample performance through numerical studies and an empirical application to risk assessment.