Time Series Analysis & Modelling
May 31, 2006, 1:15 pm in room 316. H. Rust (PIK): Confidence Intervals for Return Level Estimates -- A Bootstrap Approach Abstract: Standard return level estimation is generally based on extreme value analysis assuming independent extremes, i.e. fitting a model to excesses over threshold or annual maxima. The assumption of independence might not be justifiable in many practical applications, as for river run-off. This has consequences for the return level estimates. One effect is an increasing uncertainty. With a simulation study, we illustrate the effect of dependence on the variability of a return level estimate. The confidence intervals obtained from the asymptotic theory turned out to be too small to capture this variability. In order to obtain more reliable confidence intervals, we compare different strategies based on the bootstrap. One of the strategies yields promising results and thus its performance is studied in more detail. This semi-parametric bootstrap approach was exemplified with a case study: a confidence limit for a 100-year return level estimate from a runoff series in southern Germany was calculated and compared to the result obtained using the asymptotic distribution of the Maximum-Likelihood estimator.