Stochastic Volatily Models using Hamiltonian Monte Carlo Methods and Stan

Abstract

This paper presents a study using the Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors in the observation equation of stochastic volatility models, besides the Gaussian distribution, to address problems as heavy tails and asymmetry in the returns. Moreover, we use recently developed information criteria WAIC and LOO that approximate the cross-validation methodology, to perform the selection of models. Throughout this work, we study the quality of the HMC methods through examples, simulation studies and applications to real data sets.