Estimation of nonparametric autoregressive time series models under dynamical constraints

A method is introduced to estimate nonparametric autoregressive models under the additional constraint that its regression function has a stable cycle. It is based on a penalty approach that chooses a series expansion approximation taking into account both goodness-of-fit and fulfillment of the constraint. Consistency of the proposed estimator is obtained under general hypothesis. Feasibility and effective performance of the introduced method are studied through simulated examples and electro-encephalographic data collected from a subject suffering from epilepsy.