Forecasting with the Standardized Self-Perturbed Kalman Filter

We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted by the estimate of the measurement error variance. This avoids the calibration of a design parameter as the perturbation term is scaled by the level of uncertainty in the data. It is shown by Monte Carlo simulations that this perturbation method is associated with a good tracking of the dynamics of the parameters compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P 500 index under several model specifications, and determine the extent to which realized volatility can be used to predict excess returns.