Gamma-Driven Markov Processes and Extensions with Application to Realized Volatility

We propose a novel class of Markov processes for dealing with continuous positive time series data, which is constructed based on a latent gamma effect and named gamma-driven (GD) models. The GD processes possess desirable properties and features: (i) it can produce any desirable invariant distribution with support on R+, (ii) it is time-reversible, and (iii) it has the transition density function given in an explicit form. Estimation of parameters is performed through the maximum likelihood method combined with a Gauss Laguerre quadrature to approximate the likelihood function. The evaluation of the estimators and also confidence intervals of parameters are explored via Monte Carlo simulation studies. Two generalizations of the GD processes are also proposed to handle nonstationary and long-memory time series. We apply the proposed methodologies to analyze the daily realized volatility of the FTSE 100 equity index.