IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v11y2018i3p45-d162047.html
   My bibliography  Save this article

Stationary Threshold Vector Autoregressive Models

Author

Listed:
  • Galyna Grynkiv

    (Department of Economics, University of Western Ontario, Social Science Centre, London, ON N6A 5C2, Canada)

  • Lars Stentoft

    (Department of Economics, University of Western Ontario, Social Science Centre, London, ON N6A 5C2, Canada
    Department of Statistical and Actuarial Sciences, University of Western Ontario, Western Science Centre, London, ON N6A 5B7, Canada)

Abstract

This paper examines the steady state properties of the Threshold Vector Autoregressive model. Assuming that the trigger variable is exogenous and the regime process follows a Bernoulli distribution, necessary and sufficient conditions for the existence of stationary distribution are derived. A situation related to so-called “locally explosive models”, where the stationary distribution exists though the model is explosive in one regime, is analysed. Simulations show that locally explosive models can generate some of the key properties of financial and economic data. They also show that assessing the stationarity of threshold models based on simulations might well lead to wrong conclusions.

Suggested Citation

  • Galyna Grynkiv & Lars Stentoft, 2018. "Stationary Threshold Vector Autoregressive Models," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(3), pages 1-23, August.
  • Handle: RePEc:gam:jjrfmx:v:11:y:2018:i:3:p:45-:d:162047
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/11/3/45/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1911-8074/11/3/45/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    3. Conlisk, John, 1974. "Stability in a Random Coefficient Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(2), pages 529-533, June.
    4. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    5. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    6. Conlisk, John, 1976. "A Further Note on Stability in a Random Coefficient Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 759-764, October.
    7. Filippo Altissimo & Giovanni L. Violante, 2001. "The non-linear dynamics of output and unemployment in the U.S," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 461-486.
    8. George H. K. Wang & Jot Yau, 2000. "Trading volume, bid–ask spread, and price volatility in futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(10), pages 943-970, November.
    9. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    10. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    11. Fuchun Li & Pierre St-Amant, 2010. "Financial Stress, Monetary Policy, and Economic Activity," Bank of Canada Review, Bank of Canada, vol. 2010(Autumn), pages 9-18.
    12. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    13. 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.
    14. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    15. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    16. Ahmed Muhammad Farid & Satchell Stephen, 2018. "What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    17. Quinn, Barry G & Nicholls, Desmond F, 1981. "The Stability of Random Coefficient Autoregressive Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 741-744, October.
    18. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
    19. Barnes, Michelle L., 1999. "Inflation and returns revisited: a TAR approach," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 233-245, November.
    20. Nathan S. Balke, 2000. "Credit and Economic Activity: Credit Regimes and Nonlinear Propagation of Shocks," The Review of Economics and Statistics, MIT Press, vol. 82(2), pages 344-349, May.
    21. Peel, D A & Speight, A E H, 1998. "Modelling Business Cycle Nonlinearity in Conditional Mean and Conditional Variance: Some International and Sectoral Evidence," Economica, London School of Economics and Political Science, vol. 65(258), pages 211-229, May.
    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. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205, Edward Elgar Publishing.
    2. Pitarakis Jean-Yves, 2006. "Model Selection Uncertainty and Detection of Threshold Effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-30, March.
    3. Donayre Luiggi & Eo Yunjong & Morley James, 2018. "Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-11, February.
    4. Julius Loermann, 2018. "The Impact of CHF/EUR Exchange Rate Uncertainty on Swiss Exports to the Eurozone: Evidence from a Threshold VAR," FIW Working Paper series 189, FIW, revised Feb 2019.
    5. Pitarakis, J., 2004. "Model selection uncertainty and detection of threshold effects," Discussion Paper Series In Economics And Econometrics 0409, Economics Division, School of Social Sciences, University of Southampton.
    6. Rozina Shaheen, 2020. "Credit market conditions and impact of monetary policy in a developing economy context," International Economics and Economic Policy, Springer, vol. 17(2), pages 409-425, May.
    7. Tena, Juan de Dios & Tremayne, A.R., 2009. "Modelling monetary transmission in UK manufacturing industry," Economic Modelling, Elsevier, vol. 26(5), pages 1053-1066, September.
    8. Singh, Tarlok, 2014. "On the regime-switching and asymmetric dynamics of economic growth in the OECD countries," Research in Economics, Elsevier, vol. 68(2), pages 169-192.
    9. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    10. Mr. Magnus Saxegaard, 2006. "Excess Liquidity and Effectiveness of Monetary Policy: Evidence from Sub-Saharan Africa," IMF Working Papers 2006/115, International Monetary Fund.
    11. Renée Fry-Mckibbin & Jasmine Zheng, 2016. "Effects of the US monetary policy shocks during financial crises – a threshold vector autoregression approach," Applied Economics, Taylor & Francis Journals, vol. 48(59), pages 5802-5823, December.
    12. Simon M. Potter, 1999. "Nonlinear time series modelling: an introduction," Staff Reports 87, Federal Reserve Bank of New York.
    13. Stefan Avdjiev & Zheng Zeng, 2014. "Credit growth, monetary policy and economic activity in a three-regime TVAR model," Applied Economics, Taylor & Francis Journals, vol. 46(24), pages 2936-2951, August.
    14. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert & Taylor, A.M. Robert, 2016. "Tests for explosive financial bubbles in the presence of non-stationary volatility," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 548-574.
    15. António Afonso & Jaromír Baxa & Michal Slavík, 2018. "Fiscal developments and financial stress: a threshold VAR analysis," Empirical Economics, Springer, vol. 54(2), pages 395-423, March.
    16. Peter Martey Addo, 2014. "Multivariate Self-Exciting Threshold Autoregressive Models with eXogenous Input," Papers 1407.7738, arXiv.org.
    17. Ólan T. Henry & Peter M. Summers, 2000. "Australian Economic Growth: Nonlinearities and International Influences," The Economic Record, The Economic Society of Australia, vol. 76(235), pages 365-373, December.
    18. Baum, Anja & Koester, Gerrit B., 2011. "The impact of fiscal policy on economic activity over the business cycle - evidence from a threshold VAR analysis," Discussion Paper Series 1: Economic Studies 2011,03, Deutsche Bundesbank.
    19. Wan, Jer-Yuh & Kao, Chung-Wei, 2015. "Interactions between oil and financial markets — Do conditions of financial stress matter?," Energy Economics, Elsevier, vol. 52(PA), pages 160-175.
    20. van Dijk, Dick & Hans Franses, Philip & Peter Boswijk, H., 2007. "Absorption of shocks in nonlinear autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4206-4226, May.

    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:gam:jjrfmx:v:11:y:2018:i:3:p:45-:d:162047. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.mdpi.com/ .

    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: XML Conversion Team (email available below). General contact details of provider: https://www.mdpi.com/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.