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Bayesian mixture of autoregressive models

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  • Lau, John W.
  • So, Mike K.P.

Abstract

An infinite mixture of autoregressive models is developed. The unknown parameters in the mixture autoregressive model follow a mixture distribution, which is governed by a Dirichlet process prior. One main feature of our approach is the generalization of a finite mixture model by having the number of components unspecified. A Bayesian sampling scheme based on a weighted Chinese restaurant process is proposed to generate partitions of observations. Using the partitions, Bayesian prediction, while accounting for possible model uncertainty, determining the most probable number of mixture components, clustering of time series and outlier detection in time series, can be done. Numerical results from simulated and real data are presented to illustrate the methodology.

Suggested Citation

  • Lau, John W. & So, Mike K.P., 2008. "Bayesian mixture of autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 38-60, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:38-60
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    References listed on IDEAS

    as
    1. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    2. Peter J. Green & Sylvia Richardson, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 355-375, June.
    3. 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.
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    Cited by:

    1. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    2. Davide Ravagli & Georgi N. Boshnakov, 2022. "Bayesian analysis of mixture autoregressive models covering the complete parameter space," Computational Statistics, Springer, vol. 37(3), pages 1399-1433, July.
    3. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    4. Gonçalves Mazzeu, Joao Henrique & Ruiz Ortega, Esther & Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Ori Rosen & Sally Wood & David S. Stoffer, 2012. "AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1575-1589, December.

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