A Metropolis-in-Gibbs Sampler for Estimating Equity Market Factors

A model incorporating common Markovian regimes and GARCH residuals in a persistent factor environment is considered. Given the intractable and approximate nature of the likelihood function, a Metropolis-in-Gibbs sampler with Bayesian features is constructed for estimation purposes. The common factor drawing procedure is effectively an exact derivation of the Kalman filter with a Markovian regime component and GARCH innovations. To accelerate the drawing procedure, approximations to the conditional density of the common component are considered. The model is applied to equity data for 18 developed markets to derive global, European, and country specific equity market factors.