Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/229672
Authors: 
Lange, Rutger Jan
Year of Publication: 
2021
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2020-052/III
Abstract: 
This article presents a filter for state-space models based on Bellman's dynamic programming principle applied to the mode estimator. The proposed Bellman filter (BF) generalises the Kalman filter (KF) including its extended and iterated versions, while remaining equally inexpensive computationally. The BF is also (unlike the KF) robust under heavy-tailed observation noise and applicable to a wider range of (nonlinear and non-Gaussian) models, involving e.g. count, intensity, duration, volatility and dependence. (Hyper)parameters are estimated by numerically maximising a BF-implied log-likelihood decomposition, which is an alternative to the classic prediction-error decomposition for linear Gaussian models. Simulation studies reveal that the BF performs on par with (or even outperforms) state-of-the-art importance-sampling techniques, while requiring a fraction of the computational cost, being straightforward to implement and offering full scalability to higher dimensional state spaces.
Subjects: 
dynamic programming
curse of dimensionality
importance sampling
Laplace method
Kalman filter
maximum a posteriori (MAP) estimate
NAIS
particle filter
prediction-error decomposition
posterior mode
Viterbi algorithm
JEL: 
C32
C53
C61
Document Type: 
Working Paper

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