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On geometric ergodicity of the MTAR process

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  • Lee, Oesook
  • Shin, Dong Wan
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    Abstract

    We consider the momentum threshold autoregressive (MTAR) process and characterize the region of the autoregressive coefficients for geometric ergodicity. The region is a proper subset of the ergodic region of the TAR process. We show that the process is geometrically ergodic inside the region and is transient outside the closure of the region.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 48 (2000)
    Issue (Month): 3 (July)
    Pages: 229-237

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    Handle: RePEc:eee:stapro:v:48:y:2000:i:3:p:229-237

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    Related research

    Keywords: Asymmetry Ergodicity Nonstationarity Stationarity Transience;

    References

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    1. 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 S145-59, Supplemen.
    2. Sichel, Daniel E, 1993. "Business Cycle Asymmetry: A Deeper Look," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 224-36, April.
    3. Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
      • 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 627-45, August.
    4. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    5. Lee, Oesook, 2000. "On probabilistic properties of nonlinear ARMA(p,q) models," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 121-131, January.
    6. Pippenger, Michael K & Goering, Gregory E, 1993. "A Note on the Empirical Power of Unit Root Tests under Threshold Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(4), pages 473-81, November.
    7. 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 307-28, April.
    8. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
    9. 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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    Citations

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    Cited by:
    1. Shin, Dong Wan & Lee, Oesook, 2007. "Asymmetry and nonstationarity for a seasonal time series model," Journal of Econometrics, Elsevier, vol. 136(1), pages 89-114, January.
    2. 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.
    3. Wan Shin, Dong & Lee, Oesook, 2003. "An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models," Journal of Econometrics, Elsevier, vol. 115(1), pages 29-52, July.
    4. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.
    5. 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.

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