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Bayesian Inference Of Threshold Autoregressive Models

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  • Cathy W. S. Chen
  • Jack C. Lee

Abstract

. The study of non‐linear time series has attracted much attention in recent years. Among the models proposed, the threshold autoregressive (TAR) model and bilinear model are perhaps the most popular ones in the literature. However, the TAR model has not been widely used in practice due to the difficulty in identifying the threshold variable and in estimating the associated threshold value. The main focal point of this paper is a Bayesian analysis of the TAR model with two regimes. The desired marginal posterior densities of the threshold value and other parameters are obtained via the Gibbs sampler. This approach avoids sophisticated analytical and numerical multiple integration. It also provides an estimate of the threshold value directly without resorting to a subjective choice from various scatterplots. We illustrate the proposed methodology by using simulation experiments and analysis of a real data set.

Suggested Citation

  • Cathy W. S. Chen & Jack C. Lee, 1995. "Bayesian Inference Of Threshold Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 483-492, September.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:5:p:483-492
    DOI: 10.1111/j.1467-9892.1995.tb00248.x
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    References listed on IDEAS

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    1. Robert E. McCulloch & Ruey S. Tsay, 1994. "Bayesian Analysis Of Autoregressive Time Series Via The Gibbs Sampler," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 235-250, March.
    2. John Geweke & Nobuhiko Terui, 1993. "Bayesian Threshold Autoregressive Models For Nonlinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 441-454, September.
    3. Bradley P. Carlin & Alan E. Gelfand & Adrian F. M. Smith, 1992. "Hierarchical Bayesian Analysis of Changepoint Problems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 389-405, June.
    4. Robert E. McCulloch & Ruey S. Tsay, 1994. "Statistical Analysis Of Economic Time Series Via Markov Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 523-539, September.
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