Nonparametric filtering for stochastic nonlinear oscillations

This paper proposes a method of nonparametric filtering for stochastic nonlinear oscillations with particular interest in their derivative estimation. Based on a second-order ordinary differential equation, a stochastic oscillation is modeled by a two-variate stochastic differential equation without specifying the function form of the drift function, where the first variable is assumed to be observable but not the other. Given the discrete time series with observation error, the proposed method enables us to estimate the values of the drift function and its derivatives including those of the unobservable variable. According to the results of numerical experiments to compare estimation accuracy with a parametric method, the proposed method shows better performance in the estimation of nonlinear models.