Estimation of Hyperbolic Diffusion Using MCMC Method

Abstract

In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as slowly declining autocorrelation function of absolute terms. We demonstrate that the MCMC method provides a useful tool to analyze hyperbolic diffusions. In particular, quantities of posterior distributions obtained from MCMC outputs can be used for statistical inferences.Markov Chain Monte Carlo, Hyperbolic diffusion, Milstein approximation, ARCH, Long Memory.