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Paper No. 10-13

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JQ Smith and G Freeman

Distributional Kalman filters for Bayesian forecasting and closed form recurrences

Date: July 2010

Abstract: Over the last 50 years there has been an enormous explosion in developing full distributional analogues of the Kalman .lter. In this paper we explore some of the ways analogues of the orginal second order processes discovered by Kalman have their analogues in Bayesian state space models. Many of these analogues need to be calculated using numerical methods like MCMC so they retain, or even enhance the descriptive power of the Kalman Filter, but at a cost of transparency. However, if the analogues are drawn properly, elegant recurrence relationships - like those of the Kalman Filter - can still be developed that apply at least for one step ahead forecast distribution. In this paper we explore the variety of ways such models have been built, in particular with respect to graphical time series models..