Modeling economic time series by forward and backward state space innovation models and IV estimators

This paper shows how the backward innovation model of a weakly stationary stochastic process with rational spectra is used together with the more familiar forward innovation model to estimate system and innovation covariance matrices. It is shown that state vectors of both forward and backward innovation models can be jointly used to construct asymptotically efficient IV estimators of state space models. The paper then shows how to improve the estimates iteratively while retaining the nestedness property of the original estimators proposed by Aoki in 1987.