Nonparametric Inference of Conditional Expectile Functions in Large-Scale Time Series Data With Improved Efficiency

Expectile is a coherent and elicitable law-invariant risk measure widely applied in risk management. Existing methods based on iteratively reweighted least squares (IWLS) are not computationally efficient for large-scale sample sizes. To overcome the issue, we develop a direct nonparametric conditional expectile function estimator by inverting the local polynomial estimator of the conditional loss-gain function. The proposed estimator is computationally friendly and stable without using iterative algorithms that require computation with large-scale data in each iteration. We establish the asymptotic distribution of the proposed estimator. We further show that the proposed estimator has a smaller variance than the existing IWLS estimator and a smaller mean square error in various scenarios. Simulations confirm the computational and statistical efficiency of the proposed method. We further apply the proposed methods to an S&P500 data set to illustrate the computational time to estimate the conditional expectile-based value-at-risk (EVaR) and the precision in out-of-sample prediction.