Initializing the Kalman Filter for Nonstationary Time Series Models

Abstract. The problem of initializing the Kalman filter for nonstationary time series models is considered. Ansley and Kohn have developed a ‘modified Kalman filter’ for use with nonstationary models to produce estimates from what they call a ‘transformation approach’. We show that the same results can be obtained with a suitable initialization of the ordinary Kalman filter. Assuming there are d starting values for the nonstationary series, we initialize the Kalman filter using data through time d with the transformation approach estimate of the state vector and its associated error covariance matrix at time d . We give details of the initialization for ARIMA models, ARIMA component models and dynamic linear models. We present an example to illustrate how the results may differ from results obtained under more naive initializations that have been suggested.