Abstract
The aim of the paper is to introduce an innovative approach to conditional covariance and correlation modelling, which is useful e.g. in the multivariate GARCH context. The suggested two-step method is based on the LDL decomposition of the conditional covariance matrix and state space modelling with the associated Kalman recursions.
Together, they provide a dynamic orthogonal transformation of observed multivariate time series. This time-varying transformation indeed simplifies further (second step) conditional variance modelling of stochastic vector data due to their simultaneously uncorrelated elements.