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 (Electronics Letters 1992; 28: 558–559) for the online estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is 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 amount 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 online algorithms and to 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 determines the extent to which realized variance can be used to predict excess returns.