Bayesian time-varying quantile regression on exceedance

Abstract

ABSTRACT Exceedance analysis aims to model extreme data that are in the tail of the distribution, with these values being greater than a threshold. In this type of modelling, the tail can usually have different types of shapes. For exceedance, the extreme value theory shows that generalized Pareto distribution (GPD) is the limit distribution of sufficiently large thresholds. The studies on extreme analysis primarily focus on estimating the probability of the occurrence of extreme events, which are the values that are in the highest quantiles of the distribution. Based on this, this work proposed a quantile regression model for the GPD distribution, where the high quantiles of the distribution are written as a function of covariates. The proposed model also allows the regression parameters to vary over time. The parameter estimation of these new models is conducted under the Bayesian paradigm. Simulations are conducted to analyze the performance of our proposed models. Results of temperature applications in the USA and Brazil (environmental data) and consumer price index in Brazil (financial data) have efficiently explained how covariates influence the quantile behaviour over time.