Inference, Simulation and Application of a Latent Trawl Model for Extreme Values

Abstract

We extend the study of a parametric latent model for extreme values from Noven et al. (2018) which captures serial dependence in the exceedances above a threshold using so-called trawl processes (Barndorff-Nielsen (2011)) - a family of stationary and infinitely divisible random processes. In this regard, this article comprises a new approximation of the autocorrelation function at small lags. Applying this result, we unveil a unprecedented way to estimate key trawl parameters along with their convergence in probability to the true value under reasonable technical assumptions. We also investigate an identifiability issue from both theoretical arguments and numerical examples with a focus on a simulation study. This leads to apply this model on solar energy intake data (ARNE Mesonet station, Oklahoma, USA) with negative shape parameter which corroborates the flexibility and goodness-of-fit originally tested in Noven et al. (2018).

Keywords: trawl process, peaks-over-threshold, generalised Pareto distribution, pairwise likelihood estimation, Kullback-Leibler divergence

JEL Classification: C13, Q53