An empirical re-examination of extreme tail behavior: testing the assumptions of the power laws and the generalized Pareto distribution on the financial series

This study investigates whether the power laws and the associated generalized Pareto distribution (GPD) exist in the extreme tail behavior of financial return series. We include 10 series of five major financial categories over the period 1971–2018 for empirical analysis. For the former assumption, we test three representative power-law distributions. For the latter, we employ an innovative bootstrap goodness-of-fit test of GPD modeling. We also discuss the relationship between both assumptions. The empirical outcomes indicate that both assumptions do not necessarily hold for all tail series due to the outlying observations. The rejection of the power laws assumption leads to the rejection of the GPD assumption. This rejection does not promise the non-rejection of power laws either. However, the non-rejection of either assumption does not imply non-rejection of the other assumption. Power-law distribution and exponential distribution outperform log-normal distribution in tail fitting. GPD fits better at the 1% quantile level than at the 5% level. Overall, we need to acknowledge the considerable gap between the goodness-of-fit testing outcomes of both the power laws and GPD assumptions.