Estimation of extreme values of time series with heavy tails

The paper focuses on the development of a new method for extreme value estimation based on sampled financial time series. Of particular concern is the case when the extreme values asymptotically follow the Fréchet distribution. The method is designed to account for statistical dependence between the data points of the time series in a rational way. The proposed procedure avoids the problem of declustering of data to ensure independence, which is a common problem for the peaks-over-threshold method. The goal has been to establish an accurate method for prediction of e.g. the VaR based on recorded historical data.