Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns...

In economics, rank-size regressions provide popular estimators of tail exponents of heavy-tailed distributions. We discuss the properties of this approach when the tail of the distribution is regularly varying rather than strictly Pareto. The estimator then over-estimates the true value in the...

We use the expected lifetime range (ELR) ratio based on the extreme values of asset prices to detect the presence of mean reversion in stock returns. We find that the actual cross-sectional average of the ELR ratio is significantly less than its bootstrap means, thereby indicating a considerable...