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

ABSTRACT 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.