Forecasting with the Standardized Self-Perturbed Kalman Filter

A modification of the self-perturbed Kalman filter of Park and Jun (1992) is proposed for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is weighted by the measurement error variance, thus avoiding the calibration of a design parameter. The standardization leads to a better tracking of the dynamics of the parameters compared to other on-line methods, especially as the level of noise increases. The proposed estimation method, coupled with dynamic model averaging and selection, is adopted to forecast S&P 500 realized volatility series with a time-varying parameters HAR model with exogenous variables.