Oscillation Processes and Phase Estimation with Nonlinear State Space Models

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonpara-metric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In an extended version we also allow for a time-varying amplitude and baseline. For that situation a Rao-Blackwellized particle smoother that combines the Kalman smoother and an efficient sequential Monte Carlo smoother is suggested. The proposed algorithms are computationally efficient. The potential of the method for practical applications is demonstrated through simulations and an application to human electrocardiogram recordings.