Background I have a time series of structural loads, which are measured forces on a moored ocean buoy, and I need to obtain the return period value so that the structure can be designed to withstand the max load expected in a storm. The return period is estimated from the measured time series in the following way: First, I choose a threshold and identify the peaks above this threshold. Extreme events are expected to have a distribution known as the Generalized Pareto Distribution (GPD), so I fit the peaks to that distribution. Then the GPD fit is inverted to give the load associated with the probability of a chosen time period (3 hours). This load is called the return period value. I am using a program called WAFO, which takes extreme value analysis routines from S-Plus, to do this analysis.
Problem The problem is how to assess the quality of the return period estimate. WAFO produces quantile-quantile plots that show how well the peaks match the GPD, a p-value to check the quality of the fit, or confidence bounds on the return period estimate. But these 3 diagnostics seem to conflict. Sometimes the q-q plot shows that many peaks don't fit the GPD (bad), but the p-value for the fit is high (good) and the confidence bounds are narrow (good). Sometimes the confidence bounds are very wide (bad) but the q-q plot shows the peaks lining up with the GPD (good). My gut sense is that the quality might be poor because we only measured data for a limited duration and there is likely measurement noise.
Question: How can I tell if the return period estimate is good vs bad?