On conditional covariance modelling: An approach using state space models

A novel approach to conditional covariance modelling is introduced in the context of multivariate financial time series analysis. In particular, a class of multivariate generalized autoregressive conditional heteroscedasticity models is proposed. The suggested modelling technique is based on a specific dynamic orthogonal transformation derived by the LDL factorization of the conditional covariance matrix. An observed time series is transformed into a particular form that can be further treated by means of a discrete-time state space model under corresponding assumptions. The calibration can be performed by the associated Kalman recursive formulas, which are numerically effective. The introduced procedure has been investigated by extensive Monte Carlo experiments and empirical financial applications; it has been compared with other methods commonly used in this framework. The outlined methodology has demonstrated its capabilities, and it seems to be at least competitive in this field of research.