A Multivariate Random Walk Model with Slowly Changing Drift and Cross-correlation Applied to Finance

A new multivariate random walk model with slowly changing drift and cross-correlations for multivariate processes is introduced and investigated in detail. In the model, not only the drifts and the cross-covariances but also the cross-correlations between single series are allowed to change slowly over time. The model can accompany any number of components such as many number of assets. The model is particularly useful for modelling and forecasting the value of financial portfolios under very complex market conditions. Kernel estimation of local covariance matrix is used. The integrated effect of the estimation errors involved in estimating the integrated processes is derived. Practical relevance of the model and estimation is illustrated by application to several foreign exchange rates.