Computing the mean square error of unobserved components extracted by misspecified time series models

Algorithms are presented for computing mean square errors in a misspecified unobserved components model when the true model is known. It is assumed that both the true and misspecified models can be put in linear state space form. The algorithm for filtering is based on the Kalman filter while that for smoothing modifies the fixed-point smoother. Illustrations include the efficiency of the Hodrick-Prescott filter for annual flow data and the mean square error of predictions for misspecified models from the autoregressive integrated moving average class.