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...

Tests based on the quantile regression process can be formulated like the classical Kolmogorov-Smirnov and Cramer-von-Mises tests of goodness-of-fit employing the theory of Bessel processes as in Kiefer (1959). However, it is frequently desirable to formulate hypotheses involving unknown...