Simulation based inference on stochastic volatility models in an environmental study

Abstract

This paper examines the time series properties of the growth rate in atmospheric carbon dioxide concentrations (ACDC) using monthly data from a subset of the well-known Mauna Loa atmosphere carbon dioxide record. We consider a class of stochastic volatility (SV) models that incorporate the following features: correlations between the the monthly changes in level of ACDC growth rate and their volatility, heavy-tailed error distribution, jumps in observation equation and/or in volatility process. The purpose of this article is try to provide a unified way to understand the effect of these four factors on modelling the monthly time-series of ACDC level growth rate and find the most adequate and parsimonious model. In a Bayesian approach, we estimate a few extensions of the basic stochastic volatility model using the Markov Chain Monte Carlo (MCMC) method and compare these models using Deviance Information Criterion(DIC). Our study shows that the leverage effect is present also the SV models with independent jumps in observation equation and volatility equation perform well.