Filtering and smoothing formulas of AR(p)-modulated Poisson processes

Recursive formulas are presented to compute smoothed estimates and online filtered estimates for a hidden AR(p) processes, using modulated Poisson observations. We utilize techniques of a transformation of probability, a duality between a forward equation and a backward equation, and develop a new p...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2020-06, Vol.49 (6), p.1575-1591
Main Authors: Duan, Qihong, Liu, Junrong
Format: Article
Language:English
Subjects:
Algorithms
Autoregression model
Closed-form expression
Estimates
Filtering
Markov analysis
Numerical methods
Poisson observation
Polynomials
Reference probability
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Summary:Recursive formulas are presented to compute smoothed estimates and online filtered estimates for a hidden AR(p) processes, using modulated Poisson observations. We utilize techniques of a transformation of probability, a duality between a forward equation and a backward equation, and develop a new partial fraction decomposition of rational polynomials with several variables. The established polynomial time algorithm computes efficiently closed-form expressions of estimates for the hidden AR(p) process. With a truncating technique, complexity of the algorithm can be reduced further. Finally, we discuss some computational issues related to the proposed algorithm and compare it with other numerical methods.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2018.1501483