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Estimation of Nonparametric Autoregressive Time Series Models Under Dynamical Constraints

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  • R. J. Biscay
  • Marc Lavielle
  • Carenne Ludeña

Abstract

. 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.

Suggested Citation

  • R. J. Biscay & Marc Lavielle & Carenne Ludeña, 2005. "Estimation of Nonparametric Autoregressive Time Series Models Under Dynamical Constraints," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 371-397, May.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:3:p:371-397
    DOI: 10.1111/j.1467-9892.2004.00407.x
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    References listed on IDEAS

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    1. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    2. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    3. Young Truong & Prakash Patil, 2001. "Asymptotics for Wavelet Based Estimates of Piecewise Smooth Regression for Stationary Time Series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 159-178, March.
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