Expected Shortfall Estimation and Gaussian Inference for Infinite Variance Time Series
针对可能具有重尾的资产收益率，开发了预期短缺的非参数估计方法，通过尾部修剪实现标准高斯推断，并解决了修剪带来的偏差问题，适用于金融数据。
We develop methods of nonparametric estimation for the Expected Shortfall of possibly heavy tailed asset returns that leads to asymptotically standard inference. We use a tail-trimming indicator to dampen extremes negligibly, ensuring standard Gaussian inference, and a higher rate of convergence than without trimming when the variance is infinite. Trimming, however, causes bias in small samples and possibly asymptotically when the variance is infinite, so we exploit a rarely used remedy to estimate and utilize the tail mean that is removed by trimming. Since estimating the tail mean involves estimation of tail parameters and therefore an added arbitrary choice of the number of included extreme values, we present weak limit theory for an ES estimator that optimally selects the number of tail observations by making our estimator arbitrarily close to the untrimmed estimator, yet still asymptotically normal. Finally, we apply the new estimators to financial returns data.