Bayesian Multivariate Autoregressive Gamma Processes: An Application to Realized Volatility

Abstract

In this thesis I present the multivariate Autoregressive Gamma process introduced by Le, Singleton and Dai (2010), a model founded on the univariate ARG first introduced in Gourieroux and Jasiak (2006). I discuss its mathematical properties and provide a MCMC algorithm for the Bayesian estimation of the parameters. The gamma process has been used due to its desirable properties in modelling realized volatility, for this reason I evaluate its performance on a panel of realized volatilities for multiple assets.