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A Bayesian nonlinearity test for threshold moving average models

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  • Qiang Xia
  • Jiazhu Pan
  • Zhiqiang Zhang
  • Jinshan Liu

Abstract

We propose a Bayesian test for nonlinearity of threshold moving average (TMA) models. First, we obtain the marginal posterior densities of all parameters, including the threshold and delay, of the TMA model using Gibbs sampler with the Metropolis–Hastings algorithm. And then, we adopt reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities for MA and TMA models. Posterior evidence in favour of the TMA model indicates threshold nonlinearity. Simulation experiments and a real example show that our method works very well in distinguishing MA and TMA models.

Suggested Citation

  • Qiang Xia & Jiazhu Pan & Zhiqiang Zhang & Jinshan Liu, 2010. "A Bayesian nonlinearity test for threshold moving average models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 329-336, September.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:5:p:329-336
    DOI: 10.1111/j.1467-9892.2010.00667.x
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    References listed on IDEAS

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    1. Mohamed A. Ismail & Husni A. Charif, 2003. "Bayesian inference for threshold moving average models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 119-132.
    2. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-198, April.
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    Cited by:

    1. Xiaobing Zheng & Kun Liang & Qiang Xia & Dabin Zhang, 2022. "Best Subset Selection for Double-Threshold-Variable Autoregressive Moving-Average Models: The Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1175-1201, March.
    2. Ni Shuxia & Xia Qiang & Liu Jinshan, 2018. "Bayesian Subset Selection for Two-Threshold Variable Autoregressive Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(4), pages 1-16, September.

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