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Additive nonparametric regression with autocorrelated errors

Author

Listed:
  • Michael Smith
  • Chi‐Ming Wong
  • Robert Kohn

Abstract

A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non‐linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach also allows the selection of a suitable transformation of the dependent variable. All aspects of the model are estimated simultaneously by using the Markov chain Monte Carlo method. It is shown empirically that the approach proposed works well on several simulated and real examples.

Suggested Citation

  • Michael Smith & Chi‐Ming Wong & Robert Kohn, 1998. "Additive nonparametric regression with autocorrelated errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 311-331.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:2:p:311-331
    DOI: 10.1111/1467-9868.00127
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    Cited by:

    1. Shively, Thomas S. & Walker, Stephen G. & Damien, Paul, 2011. "Nonparametric function estimation subject to monotonicity, convexity and other shape constraints," Journal of Econometrics, Elsevier, vol. 161(2), pages 166-181, April.
    2. Yu, Keming, 2002. "Quantile regression using RJMCMC algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 303-315, August.
    3. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.
    4. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    5. Maria Durbán & Iain D. Currie, 2003. "A note on P-spline additive models with correlated errors," Computational Statistics, Springer, vol. 18(2), pages 251-262, July.
    6. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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