On‐Line Variance Estimation For The Steady State Bayesian Forecasting Model

. The Bayesian approach to forecasting provides the user with distributional information which plays an important role in decision making. However, in practice, the process variances are unknown and therefore if the model operates with fixed estimates of these variances, the distributional information can be misleading. A method is proposed in this paper which produces on‐line maximum likelihood estimates of the variances for the steady state Dynamic Linear model, whose updating employs the Kalman filter. It makes use of a one‐dimensional class I multi‐process model approach which requires a set of initial values. In the limit the variance estimates are independent of the choice of initial values, but some practical suggestions are made which enable the procedure to converge faster. A numerical illustration and a number of points relevant to the performance of the model when tested under different choices of starting values are also given.