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On inference for threshold autoregressive models

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Abstract

We provide a complete Bayesian method for analyzing a threshold autoregressive (TAR) model when the order of the model is unknown. Our approach is based on a version (Godsill (2001)) of the reversible jump algorithm of Green (1995), and the method for estimating marginal likelihood from the Metropolis-Hasting algorithm by Chib and Jeliazkov (2001). We illustrate our results with simulated data and the Wolfe’s sunspot data set.

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References

  • Besag, J. (1989). A candidate’s formula: a curious result in Bayesian prediction.Biometrika, 76(1):183.

    Article  MathSciNet  Google Scholar 

  • Broemeling, L. andCook, P. (1992). Bayesian analysis of threshold autoregressions.Communications in Statistics, Theory and Methods, 21:2459–2482.

    MATH  MathSciNet  Google Scholar 

  • Carlin, B. andChib, S. (1992). Bayesian model choice via Markov chain Monte Carlo methods.Journal of Royal Statistical Society, B, 57:473–484.

    Google Scholar 

  • Chen, C. andLee, J. (1995). Bayesian inference of threshold autoregressive models.Journal of Time Series Analysis, 16:484–492.

    MathSciNet  Google Scholar 

  • Chib, S. andJeliazkov, I. (2001). Marginal likelihood from the Metropolis-Hastings output.Journal of the American Statistical Association, 96:270–281.

    Article  MATH  MathSciNet  Google Scholar 

  • Geweke, J. andTerui, N. (1993). Bayesian threshold autoregressive models for nonlinear time series.Journal of Time Series Analysis, 14:441–454.

    MATH  MathSciNet  Google Scholar 

  • Godsill, S. (2001). On the relationship between MCMC model uncertainty methods.Journal of Computational and Graphical Statistics, 10:232–248.

    Article  MathSciNet  Google Scholar 

  • Green, P. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination.Biometrika, 82:711–732.

    Article  MATH  MathSciNet  Google Scholar 

  • Haggan, V. andOzaki, T. (1981). Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model.Biometrika, 68:189–196.

    Article  MATH  MathSciNet  Google Scholar 

  • Han, C. andCarlin, B. (2001). MCMC methods for computing Bayes factors: a comparative review.Journal of the American Statistical Association, 96:1122–1132.

    Article  Google Scholar 

  • Liu, J., Wong, W., andKong, A. (1994). Covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes.Biometrika, 81:27–40.

    Article  MATH  MathSciNet  Google Scholar 

  • McCulloch, R. andTsay, R. (1993). Bayesian analysis of threshold autoregressive processes with a random number of regimes. InProceedings of the 25th Symposium on the Interface, Michael E. Tarter and Michael D. Lock., eds., pp. 253–262.

  • Nicholls, D. andQuinn, B. (1982).Review of Random Coefficient Autoregressive Models: An Introduction, Springer Verlag, New York.

    Google Scholar 

  • Priestley, M. (1980). State-dependent models: a general approach to nonlinear time series analysis.Journal of Time Series Analysis, 1:47–71.

    MATH  MathSciNet  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics 6:461–464.

    MATH  MathSciNet  Google Scholar 

  • Subba-Rao, T. andGabr, M. (1984).Introduction to Bispectral Analysis and Bilinear Time Series Models, vol. 24. Springer-Verlag, New York.

    MATH  Google Scholar 

  • Tong, H. (1983).Threshold models in nonlinear time series analysis, Springer-Verlag, New York, 0-387-90918-4.

    Google Scholar 

  • Tong, H. (1990).Nonlinear Time Series: A Dynamical System Approach. Oxford University Press, Oxford.

    Google Scholar 

  • Troughton, P. andGodsill, S. (1998). A reversible jump sampler for autoregressive time series. InInternational Conference on Acoustics, Speech and Signal Processing, IV, pp. 2257–2260.

  • Troughton, P. andGodsill, S. (2000). MCMC methods for restoration of nonlinearity distorted autoregressive signals.Signal Processing, 81:83–97.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA, USA

    Osnat Stramer & Yu-Jau Lin

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  1. Osnat Stramer
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  2. Yu-Jau Lin
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Correspondence to Osnat Stramer.

Additional information

This research is supported in part by NSF Grant SCREMS 0112219.

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Stramer, O., Lin, YJ. On inference for threshold autoregressive models. Test 11, 55–71 (2002). https://doi.org/10.1007/BF02595729

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  • DOI: https://doi.org/10.1007/BF02595729

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