Research Project
Full description We present a novel statistical framework based on recent theoretical advancements in extreme modelling for dynamical systems. Under reasonable assumptions on the time series data (e.g., the data follow a fat-tailed Fr\'{e}chet distribution), our workflow provides more robust estimates of returns and magnitudes of successive extreme events compared to standard likelihood methods. The novelty of our workflow lies in the derivation of a generalised linear model relationship between the number of successive extremes in the sequence and the parameters of the corresponding generalised extreme value distribution. Nonstationarity of the data is addressed and poses no issue in the numerical workflow. Australian gas demand provides a well suited case-study on which we illustrate our workflow to forecast successive extremes in gas demand in a nonstationary environment.