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Functional Coefficient Autoregressive Models: Estimation and Tests of Hypotheses

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  • Rong Chen
  • Lon‐Mu Liu

Abstract

In this paper, we study nonparametric estimation and hypothesis testing procedures for the functional coefficient AR (FAR) models of the form Xt=f1(Xt−d)Xt− 1+ ... +fp(Xt−d)Xt−p+εt, first proposed by Chen and Tsay (1993). As a direct generalization of the linear AR model, the FAR model is a rich class of models that includes many useful parametric nonlinear time series models such as the threshold AR models of Tong (1983) and exponential AR models of Haggan and Ozaki (1981). We propose a local linear estimation procedure for estimating the coefficient functions and study its asymptotic properties. In addition, we propose two testing procedures. The first one tests whether all the coefficient functions are constant, i.e. whether the process is linear. The second one tests if all the coefficient functions are continuous, i.e. if any threshold type of nonlinearity presents in the process. The results of some simulation studies as well as a real example are presented.

Suggested Citation

  • Rong Chen & Lon‐Mu Liu, 2001. "Functional Coefficient Autoregressive Models: Estimation and Tests of Hypotheses," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 151-173, March.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:2:p:151-173
    DOI: 10.1111/1467-9892.00217
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    Cited by:

    1. Patrick, Joshua D. & Harvill, Jane L. & Hansen, Clifford W., 2016. "A semiparametric spatio-temporal model for solar irradiance data," Renewable Energy, Elsevier, vol. 87(P1), pages 15-30.
    2. Bruno, Giancarlo, 2008. "Forecasting Using Functional Coefficients Autoregressive Models," MPRA Paper 42335, University Library of Munich, Germany.
    3. Fabio Gobbi, 2021. "Evaluating Forecasts from State-Dependent Autoregressive Models for US GDP Growth Rate. Comparison with Alternative Approaches," Advances in Management and Applied Economics, SCIENPRESS Ltd, vol. 11(6), pages 1-7.
    4. Pan, Zhiyuan & Pettenuzzo, Davide & Wang, Yudong, 2020. "Forecasting stock returns: A predictor-constrained approach," Journal of Empirical Finance, Elsevier, vol. 55(C), pages 200-217.
    5. Harvill, Jane L. & Ray, Bonnie K., 2006. "Functional coefficient autoregressive models for vector time series," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3547-3566, August.
    6. Min Gan & C.L. Philip Chen & Long Chen & Chun-Yang Zhang, 2016. "Exploiting the interpretability and forecasting ability of the RBF-AR model for nonlinear time series," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(8), pages 1868-1876, June.
    7. Harvill, Jane L. & Ray, Bonnie K., 2005. "A note on multi-step forecasting with functional coefficient autoregressive models," International Journal of Forecasting, Elsevier, vol. 21(4), pages 717-727.
    8. Man Wang & Kun Chen & Qin Luo & Chao Cheng, 2018. "Multi-Step Inflation Prediction with Functional Coefficient Autoregressive Model," Sustainability, MDPI, vol. 10(6), pages 1-16, May.
    9. Kugiumtzis Dimitris, 2008. "Evaluation of Surrogate and Bootstrap Tests for Nonlinearity in Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-26, March.

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