Temporal dependence in extremes with dynamic models
Código: WPE – 346
Fernando Ferraz do Nascimento
Hedibert Freitas Lopes
This paper is concerned with the analysis of time series data withtemporal dependence through extreme events. This is achieved via a modelformulation that considers separately the central part and the tail of the distributions,using a two component mixture model. Extremes beyond a thresholdare assumed to follow a generalized Pareto distribution (GPD). Temporaldependence is induced by allowing to GPD parameter to vary with time. Temporalvariation and dependence is introduced at a latent level via the noveluse of dynamic linear models (DLM). Novelty lies in the time variation of theshape and scale parameter of the resulting distribution. These changes in limitingregimes as time changes reect better the data behavior, with importantgains in estimation and interpretation. The central part follows a nonparametricmixture approach. The uncertainty about the threshold is explicitlyconsidered. Posterior inference is performed through Markov Chain MonteCarlo (MCMC) methods. A variety of scenarios can be entertained and includethe possibility of alternation of presence and absence of a nite upperlimit of the distribution for dierent time periods. Simulations are carried outin order to analyze the performance of our proposed model. We also applythe proposed model to nancial time series: returns of Petrobr as stocks andSP500 index. Results show advantage of our proposal over currently entertainedmodels such as stochastic volatility, with improved estimation of highquantiles and extremes.