Modele hybrydowe MSV-MGARCH z dwoma procesami ukrytymi

In order to efficiently model the price volatility of a large number of financial assets, Osiewalski and Pajor (2007, 2009) and Osiewalski (2009) introduced multivariate hybrid MSV–MGARCH models. Their conditional covariance matrix is a product of a univariate latent process and a matrix with a simple MGARCH structure (Engle’s DCC, scalar BEKK). The proposed hybrid models are useful thanks to their good fit and ability to jointly handle as many as 50 assets. However, one latent process may be insufficient in the case of a heterogenous portfolio. In this study we propose a more general hybrid structure that uses two latent processes. We present full Bayesian inference for the model and suggest an MCMC strategy for simulations from the posterior distribution. Two formal Bayesian model comparisons are given. They show the advantages of using two latent processes. In particular, our approach is applied to jointly model the volatility of four time series: two stock indices and the prices of gold and silver. We formally compare the joint model and two separate models (for indices and for metal prices).