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Distributional Kalman filters for Bayesian forecasting and closed form recurrences
Author(s) -
Smith Jim Q.,
Freeman G.
Publication year - 2011
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1207
Subject(s) - kalman filter , markov chain monte carlo , bayesian probability , extended kalman filter , state space representation , computer science , state space , ensemble kalman filter , markov chain , fast kalman filter , monte carlo method , invariant extended kalman filter , variety (cybernetics) , transparency (behavior) , series (stratigraphy) , algorithm , econometrics , mathematics , statistics , artificial intelligence , machine learning , paleontology , computer security , biology
Over the last 50 years there has been an enormous explosion in developing full distributional analogues of the Kalman filter. In this paper we explore how some of the second‐order processes discovered by Kalman have their analogues in Bayesian state space models. Many of the analogues in the lierature need to be calculated using numerical methods like Markov chain Monte Carlo so they retain, or even enhance, the descriptive power of the Kalman filter, but at the cost of reduced 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 distributions. In this paper we explore the variety of ways such models have been built, in particular with respect to graphical time series models. Copyright © 2010 John Wiley & Sons, Ltd.