Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2020-08-27
Revision-Date: 2021-12-09
Number: 20-052/III
Author-Name: Rutger-Jan Lange
Author-Workplace-Name: Erasmus University Rotterdam
Title: Bellman Filtering for State-Space Models
Abstract: We present a new filter for state-space models based on Bellman's dynamic programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The proposed Bellman filter is a direct generalisation of the (iterated and extended) Kalman filter, but remains equally inexpensive computationally. Under suitable conditions we prove that the Bellman-filtered states are (a) stable over time and (b) contractive in quadratic mean to a small region around the true state at every time step. Constant parameters are estimated by numerically maximising a filter-implied log-likelihood decomposition. Simulation studies reveal that the Bellman filter performs on par with state-of-the-art simulation-based techniques, while requiring a fraction of the computational cost, being straightforward to implement and oering full scalability to higher dimensional state spaces. In an empirical application involving multidimensional, nonlinear and degenerate state dynamics, the Bellman filter outperforms the particle filter in terms of both parameter estimation and filtering.
Classification-JEL: C32, C53, C61
Keywords: dynamic programming, Kalman filter, particle filter, posterior mode, proximal point
File-URL: https://papers.tinbergen.nl/20052.pdf
File-Format: application/pdf
File-Size: 774.095 bytes
Handle: RePEc:tin:wpaper:20200052