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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.

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