We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns ranging from 1995-2014...

A multiple hypotheses two-stage testing for an object characterized by two separated families of hypothetical probability distributions is considered. We introduce two versions of procedure of multiple hypotheses testing in a pair of stages such that in the first stage we determine one family of...