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Bayesian Model Uncertainty In Smooth Transition Autoregressions

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  • Hedibert F. Lopes
  • Esther Salazar

Abstract

. In this paper, we propose a fully Bayesian approach to the special class of nonlinear time‐series models called the logistic smooth transition autoregressive (LSTAR) model. Initially, a Gibbs sampler is proposed for the LSTAR where the lag length, k, is kept fixed. Then, uncertainty about k is taken into account and a novel reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is proposed. We compared our RJMCMC algorithm with well‐known information criteria, such as the Akaikes̀ information criteria, the Bayesian information criteria (BIC) and the deviance information criteria. Our methodology is extensively studied against simulated and real‐time series.

Suggested Citation

  • Hedibert F. Lopes & Esther Salazar, 2006. "Bayesian Model Uncertainty In Smooth Transition Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 99-117, January.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:99-117
    DOI: 10.1111/j.1467-9892.2005.00455.x
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    1. Medeiros, Marcelo & Veiga, Alvaro, 2000. "A Flexible Coefficient Smooth Transition Time Series Model," SSE/EFI Working Paper Series in Economics and Finance 360, Stockholm School of Economics, revised 29 Apr 2004.
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    Cited by:

    1. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    2. Francesco Zanetti & Konstantinos Theodoridis, 2018. "State Dependence in Labor Market Fluctuations: Evidence, Theory, and Policy Implications," Economics Series Working Papers 856, University of Oxford, Department of Economics.
    3. Cheng, Chak Hung Jack & Chiu, Ching-Wai (Jeremy), 2016. "Nonlinearities of mortgage spreads over the business cycles," Bank of England working papers 634, Bank of England.
    4. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    5. Carlo Pizzinelli & Konstantinos Theodoridis & Francesco Zanetti, 2020. "State Dependence In Labor Market Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(3), pages 1027-1072, August.
    6. Chiu, Hsin-Yu & Chen, Ting-Fu, 2020. "Impact of volatility jumps in a mean-reverting model: Derivative pricing and empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    7. Ferrara, Laurent & Marcellino, Massimiliano & Mogliani, Matteo, 2015. "Macroeconomic forecasting during the Great Recession: The return of non-linearity?," International Journal of Forecasting, Elsevier, vol. 31(3), pages 664-679.
    8. Xiwen Bai & Jesús Fernández-Villaverde & Yiliang Li & Francesco Zanetti, 2024. "The Causal Effects of Global Supply Chain Disruptions on Macroeconomic Outcomes: Evidence and Theory," Economics Series Working Papers 1033, University of Oxford, Department of Economics.
    9. Lin, Edward M.H. & Chen, Cathy W.S. & Gerlach, Richard, 2012. "Forecasting volatility with asymmetric smooth transition dynamic range models," International Journal of Forecasting, Elsevier, vol. 28(2), pages 384-399.
    10. Glen Livingston Jr & Darfiana Nur, 2020. "Bayesian estimation and model selection of a multivariate smooth transition autoregressive model," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.
    11. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    12. Wang, Jianqiang C. & Holan, Scott H., 2012. "Bayesian multi-regime smooth transition regression with ordered categorical variables," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4165-4179.
    13. Barnett, Alina & Mumtaz, Haroon & Theodoridis, Konstantinos, 2014. "Forecasting UK GDP growth and inflation under structural change. A comparison of models with time-varying parameters," International Journal of Forecasting, Elsevier, vol. 30(1), pages 129-143.
    14. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    15. Engemann, Kristie M. & Owyang, Michael T., 2010. "Whatever Happened To The Business Cycle? A Bayesian Analysis Of Jobless Recoveries," Macroeconomic Dynamics, Cambridge University Press, vol. 14(5), pages 709-726, November.
    16. Martin Bruns & Michele Piffer, 2021. "Monetary policy shocks over the business cycle: Extending the Smooth Transition framework," University of East Anglia School of Economics Working Paper Series 2021-07, School of Economics, University of East Anglia, Norwich, UK..
    17. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    18. Glen Livingston & Darfiana Nur, 2020. "Bayesian inference of smooth transition autoregressive (STAR)(k)–GARCH(l, m) models," Statistical Papers, Springer, vol. 61(6), pages 2449-2482, December.
    19. Ringwald, Leopold & Zörner, Thomas O., 2023. "The money-inflation nexus revisited," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 293-333.
    20. Muhammad Jaffri Mohd Nasir & Ramzan Nazim Khan & Gopalan Nair & Darfiana Nur, 2024. "Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model," Statistical Papers, Springer, vol. 65(5), pages 2973-3006, July.

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