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

Abstract

This paper describes a moments estimator for a standard state-space model with coefficients generated by a random walk. The method calculates the conditional expectations of the coefficients, given the observations. A penalized least squares estimation is linked to the GLS (Aitken) estimates of the corresponding linear model with time-invariant parameters. The estimates are moments estimates. They do not require the disturbances to be Gaussian, but if they are, the 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 filter proposed here is two sided and therefore uses more of the available information for estimating intermediate states. Further, the proposed filter has a clear descriptive interpretation.