Bayesian Modeling of Dynamic Extreme Values: Extension of Generalized Extreme Value Distributions with Latent Stochastic Processes

This paper develops Bayesian inference of extreme value models with a exible time- dependent latent structure. The generalized extreme value distribution is utilized to incorporate state variables that follow an autoregressive moving average (ARMA) process with Gumbel-distributed innovations. The time-dependent extreme value distribution is combined with heavy-tailed error terms. An efficient Markov chain Monte Carlo algorithm is proposed using a state space representation with a mixture of normal distribution approximating the Gumbel distribution. The methodology is illustrated using extreme data of stock returns and electricity demand. Estimation results show the usefulness of the proposed model and evidence that the latent autoregressive process and heavy-tailed errors plays an important role to describe the monthly series of minimum stock returns and maximum electricity demand.