The effect of long-range dependence on modelling extremes with the generalised extreme value distribution

Two effects arise for the modelling of block maxima from dependent time series: a reduced rate of convergence for the block maxima probability distribution towards the generalised extreme value distribution, and an increase in uncertainty of the parameter estimates compared to independent or short range dependent records. These effects are exemplified with a simulation study using a white noise, a short-range and a long-range dependent process. The two issues raised turned out to be relatively unproblematic for short-range dependent processes. For long-range dependent processes, especially the increased parameter uncertainty poses a problem. Incautious use of standard procedures would lead to a severe underestimation of the parameter uncertainty which implies a misconception of accuracy for derived quantities, such as return levels which are frequently used for risk assessment and dimensioning of hydraulic structures.