How to improve GPD fit (fitgenpar)?

[ke]

In an extreme value analysis, I used the Poisson and MRL criteria to identify a threshold, then fit the Generalized Pareto Distribution (fitgenpar) to the peaks above the chosen threshold. The threshold appears reasonable on the dispersion index and MRL plots, but the quantile-quantile plot shows that the fit is poor for the higher values. On the QQ plot, the lower values lie on a line indicating a good fit, but the higher values lie on another line. Does this mean I should manually choose a higher threshold?