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Bellman filtering for state-space models

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Document pages: 24 pages

Abstract: This article presents a filter for state-space models based on Bellman sdynamic programming principle applied to the mode estimator. The proposedBellman filter (BF) generalises the Kalman filter (KF) including its extendedand iterated versions, while remaining equally inexpensive computationally. TheBF is also (unlike the KF) robust under heavy-tailed observation noise andapplicable to a wider range of (nonlinear and non-Gaussian) models, involvinge.g. count, intensity, duration, volatility and dependence. (Hyper)parametersare estimated by numerically maximising a BF-implied log-likelihooddecomposition, which is an alternative to the classic prediction-errordecomposition for linear Gaussian models. Simulation studies reveal that the BFperforms on par with (or even outperforms) state-of-the-art importance-samplingtechniques, while requiring a fraction of the computational cost, beingstraightforward to implement and offering full scalability to higherdimensional state spaces.

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