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Functional coefficient autoregressive models: Estimation and tests of hypotheses

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  • Chen, Rong

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 successful parametric nonlinear time series models such as the threshold AR models of Tong (1983), exponential AR models of Haggan and Ozaki (1978) and many others. 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). Some simulation results are presented.

Suggested Citation

  • Chen, Rong, 1998. "Functional coefficient autoregressive models: Estimation and tests of hypotheses," SFB 373 Discussion Papers 1998,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199810
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    References listed on IDEAS

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    1. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    2. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    3. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    4. Härdle, Wolfgang & Lütkepohl, H. & Chen, R., 1996. "A Review of Nonparametric Time Series Analysis," SFB 373 Discussion Papers 1996,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. 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.
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