Estimation of and Inference about the Expected Shortfall for Time Series with Infinite Variance

We study estimation and inference of Expected Shortfall (ES) for time series with Infinite variance. The rate of convergence is determined by the tail thickness parameter and the limiting distribution is in the stable class with parameters depending on the tail thickness parameter of the time series and on the dependence structure, which makes inference complicated. A subsampling procedure is proposed to carry out statistical inference. We also analyze a nonparametric estimator of conditional expected shortfall