IDEAS home Printed from https://ideas.repec.org/a/bpj/jtsmet/v3y2011i2n1.html
   My bibliography  Save this article

Some New Results for Threshold AR(1) Models

Author

Listed:
  • Knight John

    (The University of Western Ontario)

  • Satchell Stephen

    (Trinity College, University of Cambridge and University of Sydney)

Abstract

The purpose of this paper is to derive some new results for threshold models. We consider AR(1) threshold models, with either self-exciting or exogenous triggers. In the latter case, we derive necessary and sufficient conditions for the existence of a stationary distribution, which are wider than the sufficient conditions that are the consequence of theorems provided in the literature by previous authors. We note that there appear to be no results in the literature for closed-form expressions for steady-state distributions for threshold models under econometrically relevant conditions. We provide such a result for the case of a threshold AR(1) with an exogenous trigger variable and normal innovations. It turns out to be a known distribution, namely, a compound geometric sum of normals.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:2:n:1
    as

    Download full text from publisher

    File URL: https://www.degruyter.com/view/j/jtse.2011.3.2/jtse.2011.3.2.1085/jtse.2011.3.2.1085.xml?format=INT
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    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. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    2. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(5), pages 813-843, October.
    3. Koop, Gary & Potter, Simon M, 2003. "Bayesian Analysis of Endogenous Delay Threshold Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 93-103, January.
    4. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-1042, November.
    5. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    6. Brooks, Chris, 2001. "A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 135-143, March.
    7. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    8. Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-484, November.
    9. A. J. Khadaroo, 2005. "A threshold in inflation dynamics: evidence from emerging countries," Applied Economics, Taylor & Francis Journals, vol. 37(6), pages 719-723.
    10. Salgado, Maria José S. & Garcia, Márcio G. P. & Medeiros, Marcelo C., 2005. "Monetary Policy During Brazil´s Real Plan: Estimating the Central Bank´s Reaction Function," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 59(1), January.
    11. Chen, Cathy W. S. & Chiang, Thomas C. & So, Mike K. P., 2003. "Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model," Journal of Economics and Business, Elsevier, vol. 55(5-6), pages 487-502.
    12. David McMillan, 2001. "Non-Linear Predictability of Stock Market Returns: Evidence from Non-Parametric and Threshold Models," Discussion Paper Series, School of Economics and Finance 200102, School of Economics and Finance, University of St Andrews.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:gam:jjrfmx:v:12:y:2019:i:3:p:123-:d:250648 is not listed on IDEAS
    2. repec:bpj:jtsmet:v:10:y:2018:i:2:p:22:n:1 is not listed on IDEAS
    3. McKenzie, Michael & Satchell, Stephen & Wongwachara, Warapong, 2014. "Converting true returns into reported returns: A general theory of linear smoothing and anti-smoothing," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 215-229.
    4. McKenzie, Michael & Satchell, Stephen & Wongwachara, Warapong, 2012. "Nonlinearity and smoothing in venture capital performance data," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 782-795.
    5. 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.
    6. repec:gam:jjrfmx:v:11:y:2018:i:3:p:45-:d:162047 is not listed on IDEAS
    7. John Knight & Stephen Satchell & Nandini Srivastava, 2012. "Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications," Birkbeck Working Papers in Economics and Finance 1208, Birkbeck, Department of Economics, Mathematics & Statistics.

    More about this item

    Statistics

    Access and download statistics

    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:bpj:jtsmet:v:3:y:2011:i:2:n:1. 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: (Peter Golla). General contact details of provider: https://www.degruyter.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 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.

    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.