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 nonparametric 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 particular the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient. The method is applied to human electrocardiogram recordings.
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