ARTICLE
ABSTRACT
In the case of a large portfolio, the existing models of time-varying multivariate volatility are either too simple from the financial perspective or too complex from the numerical angle. Thus, in the paper a new hybrid class of models for n-variate financial time series is proposed. The hybrid specifications are based on two simple structures: the stochastic discount factor model (SDF) from the MSV class and the scalar BEKK(1,1) model from the MGARCH class. Type I and II hybrid models are defined; both allow for different dynamics of each conditional variance or covariance (like BEKK) and keep just one latent process in the conditional covariance matrix in order to describe outliers (like SDF). For the purpose of Bayesian posterior and predictive analyses, the simulation approach based on Gibbs sampling is proposed and approximations unavoidable in the case of large n are suggested.
KEYWORDS
Bayesian econometrics, Gibbs sampling, time-varying volatility, multivariate GARCH processes, multivariate SV processes
REFERENCES
[1] Bauwens L., Laurent S., Rombouts J.V.K., [2006], Multivariate GARCH models: A survey, „Journal of Applied Econometrics” 21, 79-109.
[2] Engle R., [2002], Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, „Journal of Business and Economic Statistics” 20, 339–350.
[3] Jacquier E., Polson N., Rossi P., [1995], Models and prior distributions for multivariate stochastic volatility, technical report, University of Chicago, Graduate School of Business.
[4] O’Hagan A., [1994], Bayesian Inference, Edward Arnold, London.
[5] Osiewalski J., Pajor A., [2007], Flexibility and parsimony in multivariate financial modelling: a hybrid bivariate DCC–SV model, in: Milo W. and Wdowiński P. (ed.), Financial Markets. Principles of Modeling, Forecasting and Decision-Making (FindEcon Monograph Series No. 3), Łódź University Press, Łódź 2007 (11-26).
[6] Osiewalski J., Pajor A., Pipień M., [2007], Bayesian comparison of bivariate GARCH, SV and hybrid models, in: Welfe W. and Welfe A. (ed.), MACROMODELS’2006, Proceedings of the 33rd International Conference, Łódź 2007 (247-277).
