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Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach

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  • Man-Suk Oh
  • Dong Wan Shin

Abstract

A Markov chain Monte Carlo (MCMC) approach, called a reversible jump MCMC, is employed in model selection and parameter estimation for possibly non-stationary and non-linear time series data. The non-linear structure is modelled by the asymmetric momentum threshold autoregressive process (MTAR) of Enders & Granger (1998) or by the asymmetric self-exciting threshold autoregressive process (SETAR) of Tong (1990). The non-stationary and non-linear feature is represented by the MTAR (or SETAR) model in which one ( „ 1 ) of the AR coefficients is greater than one, and the other ( „ 2 ) is smaller than one. The other non-stationary and linear, stationary and nonlinear, and stationary and linear features, represented respectively by ( „ 1 = „ 2 = 1 ), ( „ 1 p „ 2 < 1 ) and ( „ 1 = „ 2 < 1 ), are also considered as possible models. The reversible jump MCMC provides estimates of posterior probabilities for these four different models as well as estimates of the AR coefficients „ 1 and „ 2 . The proposed method is illustrated by analysing six series of US interest rates in terms of model selection, parameter estimation, and forecasting.

Suggested Citation

  • Man-Suk Oh & Dong Wan Shin, 2002. "Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 771-789.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:771-789
    DOI: 10.1080/02664760120098829
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    1. Koop, Gary & Potter, Simon M, 1999. "Dynamic Asymmetries in U.S. Unemployment," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 298-312, July.
    2. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    3. Shin, Dong Wan & Lee, Oesook, 2001. "Tests for Asymmetry in Possibly Nonstationary Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 233-244, April.
    4. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    5. Sichel, Daniel E, 1993. "Business Cycle Asymmetry: A Deeper Look," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 224-236, April.
    6. Oh, Man-Suk, 1999. "Estimation of posterior density functions from a posterior sample," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 411-427, February.
    7. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 145-159, Supplemen.
    8. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    9. Lee, Oesook & Shin, Dong Wan, 2001. "A note on stationarity of the MTAR process on the boundary of the stationarity region," Economics Letters, Elsevier, vol. 73(3), pages 263-268, December.
    10. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    11. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
    12. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
    13. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    14. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    15. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
    16. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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