Time-varying correlations in multivariate unobserved components time series models

Multivariate unobserved components time series models can accommodate dynamic relations between dependent variables by introducing nonzero correlations between the disturbances that drive the dynamics of the components. The usual assumption of time-invariant correlations can be rather strong for many applications. In this study, we introduce a time-varying correlation parameter that allows the dynamic relations to change over time. We treat the parameter as a dynamic unobserved component. The resulting nonlinear model requires nonlinear methods for parameter estimation and filtering. For parameter estimation, we propose an indirect inference approach based on an auxiliary model using a cubic spline for the time-varying correlation. For the filtering of the time-varying correlation, a bootstrap filter is employed jointly with the technique of Rao–Blackwellization. A Monte Carlo simulation study shows that our proposed methodology is successful in both estimation and filtering. In our empirical study, we explore the strong dependence between monthly unemployment in the labour force and claimant counts. We find strong evidence that the underlying correlations are time-varying.