Factor stochastic volatility with time varying loadings and Markov switching regimes

Abstract

We generalize the factor stochastic volatility (FSV) model of Pitt and Shephard [1999. Time varying covariances: a factor stochastic volatility approach (with discussion). In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, vol. 6, Oxford University Press, London, pp. 547–570.] and Aguilar and West [2000. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. J. Business Econom. Statist. 18, 338–357.] in two important directions. First, we make the FSV model more flexible and able to capture more general time-varying variance–covariance structures by letting the matrix of factor loadings to be time dependent. Secondly, we entertain FSV models with jumps in the common factors volatilities through So, Lam and Li's [1998. A stochastic volatility model with Markov switching. J. Business Econom. Statist. 16, 244–253.] Markov switching stochastic volatility model. Novel Markov Chain Monte Carlo algorithms are derived for both classes of models. We apply our methodology to two illustrative situations: daily exchange rate returns [Aguilar, O., West, M., 2000. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. J. Business Econom. Statist. 18, 338–357.] and Latin American stock returns [Lopes, H.F., Migon, H.S., 2002. Comovements and contagion in emergent markets: stock indexes volatilities. In: Gatsonis, C., Kass, R.E., Carriquiry, A.L., Gelman, A., Verdinelli, I. Pauler, D., Higdon, D. (Eds.), Case Studies in Bayesian Statistics, vol. 6, pp. 287–302].