Applied Mathematics & Information Sciences

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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.

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