Robust Kalman–Fuller Filtering and Trend Estimation

This paper proposes a new filter based on state-space modelling that does not require strict assumptions on the innovations of the observation and transition equations. In this sense, they are robust to model misspecifications. They are recursive relations like those of the Kalman filter but derived by applying the ordinary least squares method to Fuller ’s [ 1996 . Introduction to Statistical Time Series. John Wiley & Sons] representation of the state-space model. These recursions are called the robust Kalman–Fuller filter (RKFF). Using the RKFF, this paper devises a smoother that employs all or part of the information in the sample, called the robust Kalman–Fuller smoother. This paper applies the robust Kalman filter and smoother to trend estimation of macroeconomic time series. Extensive simulation results confirm their good finite-sample performance relative to existing procedures. The new trend estimation methods are applied to US real GDP and its components.