A New Approach to the Construction of the APF Algorithm by Applying the Pearson Curves Technique

Authors

Katarzyna Brzozowska-Rup, Faculty of Management and Computer Modelling, Kielce University of Technology, PolandFollow
Antoni Leon Dawidowicz, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak´ow, PolandFollow

Author Country (or Countries)

Poland

Abstract

We consider the theoretical question concerning time series which arises when the distribution of the observed variable is in fact a conditional distribution. The Kalman filter provides an effective solution to the linear Gaussian filtering problem. However, when state or measurement, or both, are highly non-linear, and posterior probability distribution of the state is non-Gaussian, the optimal linear filter and its modifications do not provide satisfactory results. The Sequential Monte Carlo method (SMC) have become one of the familiar tools that allowed the Bayesian paradigm to be applied to approximation of sophisticated models. In this paper we propose a novel construction of an auxiliary particle filter (APF) algorithm using the Pearson curves technique (PC) for approximation of importance weights of simulated particles. The effectiveness of the method is discussed and illustrated by numerical results based on the simulated stochastic volatility process SV.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100303

Recommended Citation

Brzozowska-Rup, Katarzyna and Leon Dawidowicz, Antoni (2016) "A New Approach to the Construction of the APF Algorithm by Applying the Pearson Curves Technique," Applied Mathematics & Information Sciences: Vol. 10: Iss. 3, Article 3.
DOI: http://dx.doi.org/10.18576/amis/100303
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss3/3