  A novel numerical method for the estimation of large time-varying parameter
(TVP) models is proposed. The updating and smoothing estimates of the TVP model
are derived within the context of generalised linear least squares and through
numerically stable orthogonal transformations. The method developed is based on
computationally efficient strategies. The computational cost is reduced by
exploiting the special sparse structure of the TVP model and by utilising
previous computations. The proposed method is also extended to the rolling
window estimation of the TVP model. Experimental results show the effectiveness
of the new updating, window and smoothing strategies in high dimensions when a
large number of covariates and regressions are included in the TVP model.
