IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v14y2012i1d10.1007_s11009-010-9166-y.html
   My bibliography  Save this article

Local Unit Roots and Global Stationarity of TARMA Models

Author

Listed:
  • Marcella Niglio

    (University of Salerno
    University of Salerno)

  • Cosimo Damiano Vitale

    (University of Salerno)

Abstract

In this paper the (strict and weak) stationarity of threshold autoregressive moving average models is discussed. After examining the strict stationarity, mainly based on the random coefficient autoregressive representation of the model, we provide sufficient conditions for its weak stationarity that allow to obtain a wider stationarity region with respect to some previous results given in the literature. These conditions are discussed to distinguish between global and local stationarity, whose relation has been considered in detail. The threshold process has been further evaluated to face the problem related to the so called existence of a threshold structure in the data generating process that is strictly related to the stationarity and has significant relevance when the parameters of the model have to be estimated.

Suggested Citation

  • Marcella Niglio & Cosimo Damiano Vitale, 2012. "Local Unit Roots and Global Stationarity of TARMA Models," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 17-34, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9166-y
    DOI: 10.1007/s11009-010-9166-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-010-9166-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-010-9166-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Frederic Bec & Melika Ben Salem & Marine Carrasco, 2004. "Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 382-395, October.
    3. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    4. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    5. Stelzer, Robert, 2009. "On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity," Econometric Theory, Cambridge University Press, vol. 25(1), pages 43-62, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cathy Chen & Shu-Yu Chen & Sangyeol Lee, 2013. "Bayesian Unit Root Test in Double Threshold Heteroskedastic Models," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 471-490, December.
    2. Zisimos Koustas & Jean-Francois Lamarche, 2005. "Policy-Induced Mean Reversion in the Real Interest Rate?," Working Papers 0503, Brock University, Department of Economics, revised Jul 2005.
    3. Chevallier, Julien, 2011. "Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models," Economic Modelling, Elsevier, vol. 28(6), pages 2634-2656.
    4. Joon Y. Park & Mototsugu Shintani, 2005. "Testing for a Unit Root against Transitional Autoregressive Models," Vanderbilt University Department of Economics Working Papers 05010, Vanderbilt University Department of Economics.
    5. Koustas, Zisimos & Lamarche, Jean-François & Serletis, Apostolos, 2008. "Threshold random walks in the US stock market," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 43-48.
    6. Dilem Yildirim & Ralf Becker & Denise R Osborn, 2009. "Bootstrap Unit Root Tests for Nonlinear Threshold Models," Economics Discussion Paper Series 0915, Economics, The University of Manchester.
    7. Daiki Maki & Shin-ichi Kitasaka, 2015. "Residual-based tests for cointegration with three-regime TAR adjustment," Empirical Economics, Springer, vol. 48(3), pages 1013-1054, May.
    8. Yoon, Gawon, 2010. "Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?," Economic Modelling, Elsevier, vol. 27(2), pages 605-612, March.
    9. Ahmad Jameel Khadaroo, 2016. "Current Account Deficit in Mauritius: Risks and Prospects," South African Journal of Economics, Economic Society of South Africa, vol. 84(1), pages 109-128, March.
    10. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.
    11. Maki Daiki, 2010. "Detection of Stationarity in Nonlinear Processes: A Comparison between Structural Breaks and Three-Regime TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-43, September.
    12. Jyh‐Lin Wu & Pei‐Fen Chen & Ching‐Nun Lee, 2009. "Purchasing Power Parity, Productivity Differentials And Non‐Linearity," Manchester School, University of Manchester, vol. 77(3), pages 271-287, June.
    13. Pelin ÖGE GÜNEY, 2013. "The Term Structure of Interest Rates: A Cointegration Analysis in the Non-Linear STAR Framework," Journal of Economics and Behavioral Studies, AMH International, vol. 5(12), pages 851-860.
    14. Sergio H. Lence & GianCarlo Moschini & Fabio Gaetano Santeramo, 2018. "Threshold cointegration and spatial price transmission when expectations matter," Agricultural Economics, International Association of Agricultural Economists, vol. 49(1), pages 25-39, January.
    15. Daiki Maki, 2008. "The Performance of Variance Ratio Unit Root Tests Under Nonlinear Stationary TAR and STAR Processes: Evidence from Monte Carlo Simulations and Applications," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 77-94, February.
    16. Rodolphe Blavy & Luciana Juvenal, 2009. "Mexico's integration into NAFTA markets: a view from sectoral real exchange rates," Review, Federal Reserve Bank of St. Louis, vol. 91(Sep), pages 441-464.
    17. Andrew Phiri, 2017. "Nonlinear adjustment effects in the purchasing power parity," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 60(2), pages 14-38.
    18. Andy Snell & George Kapetanios & Yongcheol Shin, 2004. "Testing for nonlinear cointegration between stock prices and dividends," Money Macro and Finance (MMF) Research Group Conference 2003 90, Money Macro and Finance Research Group.
    19. Hai Long Vo & Duc Hong Vo, 2023. "The purchasing power parity and exchange‐rate economics half a century on," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 446-479, April.
    20. Bec, Frédérique & Zeng, Songlin, 2013. "Are Southeast Asian real exchange rates mean reverting?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 23(C), pages 265-282.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9166-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.