VC: A method for estimating time-varying coefficients in linear models

This paper describes a moments estimator for a standard state-space model with coefficients generated by a random walk. A penalized least squares estimation is linked to the GLS (Aitken) estimates of the corresponding linear model with time-invariant parameters. The VC estimator is a moments estimator that does not require the disturbances be Gaussian, but if they are, its estimates are asymptotically equivalent to maximum likelihood estimates. In contrast to Kalman filtering, no specification of an initial state or an initial covariance matrix is required. While the Kalman filter is one-sided, the VC filter is two-sided and uses more of the available information for estimating intermediate states. Further, the VC filter has a clear descriptive interpretation.