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Estimation of Nonparametric Autoregressive Time Series Models Under Dynamical Constraints
Author(s) -
Biscay R. J.,
Lavielle Marc,
Ludeña Carenne
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.00407.x
Subject(s) - autoregressive model , mathematics , estimator , nonparametric statistics , series (stratigraphy) , constraint (computer aided design) , star model , consistency (knowledge bases) , nonparametric regression , goodness of fit , nonlinear autoregressive exogenous model , econometrics , time series , mathematical optimization , statistics , autoregressive integrated moving average , paleontology , geometry , biology
. 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.