Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Does mixed frequency vector error correction model add relevant information to exchange misalignment calculus? Evidence for United States

Real exchange rate is an important macroeconomic price in the economy and a ects economic activity, interest rates, domestic prices, trade and investiments ows among other variables. Methodologies have been developed in empirical exchange rate misalignment studies to evaluate whether a real e ective exchange is overvalued or undervalued. There is a vast body of literature on the determinants of long-term real exchange rates and on empirical strategies to implement the equilibrium norms obtained from theoretical models. This study seeks to contribute to this literature by showing that it is possible to calculate the misalignment from a mixed ointegrated vector error correction framework. An empirical exercise using United States' real exchange rate data is performed. The results suggest that the model with mixed frequency data is preferred to the models with same frequency variables