Asymptotic Excess Distribution for Time Series

Both in insurance and finance applications, questions involving extremal events such as large insurance claims, large fluctuations in financial data, stock market shocks, and risk management among others play an increasingly important role in Extreme Value Modelling, Tail data are often modeled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold u is fixed and a GPD is fitted to the data exceeding u. We considered simulations from ARMA (1,1), ARCH(1) and GARCH(1,1) processes for both normal and t-distributions and using various thresholds to obtain about 20%, 10%, 5% and 1% of data above threshold u and estimated the GPD parameters using the Maximum Likelihood Method. As an application we studied a data set for foreign exchange rate returns. THIS BOOK IS WORTH BUYING FOR THE USE OF MODELLING LARGE DATA, FINANCIAL DATA AND EXTREMAL EVENTS AS WELL AS ECONOMETRIC STUDIES.