A data-cleaning augmented Kalman filter for robust estimation of state space models

A robust augmented Kalman filter (AKF) is presented for the general state space model featuring non-stationary and regression effects. The robust filter shrinks the observations towards their one-step-ahead prediction based on the past, by bounding the effect of the information carried by a new observation according to an influence function. When maximum likelihood estimation is carried out on the replacement data, an M-type estimator is obtained. The performance of the robust AKF is investigated in two applications using as a modeling framework the basic structural time series model-a popular unobserved components model in the analysis of seasonal time series. First, a Monte Carlo experiment is conducted in order to evaluate the comparative accuracy of the proposed method for estimating the variance parameters. Second, the method is applied in a forecasting context to a large set of European trade statistics series.