Nonparametric multi-step prediction in nonlinear state space dynamic systems

Jean-Pierre Vila

Filtering and smoothing of stochastic state space dynamic systems have benefited from several generations of estimation approaches since the seminal works ol Kalman in the sixties. A set of global analytical or numerical methods are now available, as the well known sequential Monte Carlo particle methods which offer some theoretical convergence results for both types of problem. However save in the case of linear Gaussian systems, objectives of the third kind objectives, which aim at estimating time steps ahead the anticipated probability density function of the system state variables, conditional on past and present system output observations, still raise theoretical and practical difficulties. The aim of this paper is to propose a nonparametric particle multi-step prediction method able to consistently estimate such anticipated conditional pdf of the state variables as well as their expectations.

Mots clés: State space dynamic systems; Prediction; Filtering; Smoothing; Kernel density estimators

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Jean-Pierre Vila. Nonparametric multi-step prediction in nonlinear state space dynamic systems. Statistics and Probability Letters, 2010, 81 (1), pp.71. ⟨10.1016/j.spl.2010.09.020⟩. ⟨hal-00698852⟩