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A Bayesian Approach To Estimating And Forecasting Additive Nonparametric Autoregressive Models

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  • Chi‐ming Wong
  • Robert Kohn

Abstract

. We present a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines. Our approach is robust to innovation outliers; it can handle missing observations and produce multistep ahead forecasts. The computation is carried out using Markov chain Monte Carlo and requires O(nM) operations where n is the sample size and M is the number of Markov chain iterations. This makes it the first exact algorithm for spline smoothing of an additive autoregressive model which can handle large data sets. The properties of the estimates and forecasts are studied empirically using simulated and real data sets.

Suggested Citation

  • Chi‐ming Wong & Robert Kohn, 1996. "A Bayesian Approach To Estimating And Forecasting Additive Nonparametric Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(2), pages 203-220, March.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:2:p:203-220
    DOI: 10.1111/j.1467-9892.1996.tb00273.x
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    Cited by:

    1. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    2. Matthew Heiner & Athanasios Kottas, 2022. "Autoregressive density modeling with the Gaussian process mixture transition distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 157-177, March.
    3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    4. Shao, Zhen & Gao, Fei & Yang, Shan-Lin & Yu, Ben-gong, 2015. "A new semiparametric and EEMD based framework for mid-term electricity demand forecasting in China: Hidden characteristic extraction and probability density prediction," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 876-889.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. King Chi Hung & Siu Hung Cheung & Wai-Sum Chan & Li-Xin Zhang, 2009. "On a robust test for SETAR-type nonlinearity in time series analysis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(5), pages 445-464.

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