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Threshold unit root models

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  • González, M.
  • Gonzalo, Jesús

Abstract

One of the main criticisms of unit root models is based on the theoretical fact that economic variables measured in rates cannot have unit roots. Nevertheless, standard unit root tests do not reject the existence of unit roots in many of those variables. In this paper we present a class of threshold models capable of replicating the behavior of economic variables such as unemployment, inflation and interest rates. Depending on the values of a threshold variable these models can have either a unit root or a stable root. However, despite the presence of the unit root, we prove they are stationary and geometrically ergodic. Least squares estimates of the parameters of these models are shown to be consistent and asymptotically normal. We propose the supremum of a e test in order to test the null of no threshold against the alternative of threshold when the threshold value is unknown. The limiting distribution is derived under the null of I (0) as well as under the null of 1(1). Critical values for both asymptotic distributions are computed and a finite sample study of the performance (size and power) of the tests developed in this paper is made. The paper concludes with an application to interest rates.

Suggested Citation

  • González, M. & Gonzalo, Jesús, 1997. "Threshold unit root models," DES - Working Papers. Statistics and Econometrics. WS 6214, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6214
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    References listed on IDEAS

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    1. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    2. 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.
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    4. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    5. Jesus Gonzalo & Tae‐Hwy Lee, 1996. "RELATIVE POWER OF t TYPE TESTS FOR STATIONARY AND UNIT ROOT PROCESSES," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(1), pages 37-47, January.
    6. 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. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
    2. Ming Chien Lo & Eric Zivot, 1999. "Threshold Cointegration and Nonlinear Adjustment to the Law of One Price," Working Papers 0030, University of Washington, Department of Economics.
    3. Dipak Ghosh & Swarna (Bashu) Dutt, . "Nonstationarity and Nonlinearity in the US Unemployment Rate: A Re-examination," Journal for Economic Educators, Middle Tennessee State University, Business and Economic Research Center.
    4. 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.
    5. 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.
    6. Muhammad Farid Ahmed & Stephen Satchell, 2019. "Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity," JRFM, MDPI, vol. 12(3), pages 1-18, July.
    7. 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.
    8. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Testing for sign and amplitude asymmetries using threshold autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 623-654, April.
    9. BESSEC Marie, 2010. "The Asymmetric Exchange Rate Dynamics in the EMS: a Time-Varying Threshold Test," EcoMod2003 330700015, EcoMod.
    10. 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.
    11. Martinez Oscar & Olmo Jose, 2012. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-39, September.
    12. Henry, Olan T. & Shields, Kalvinder, 2004. "Is there a unit root in inflation?," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 481-500, September.
    13. González, Martín & Gonzalo, Jesús, 2000. "Econometric implications of non-exact present value models," DE - Documentos de Trabajo. Economía. DE 16009, Universidad Carlos III de Madrid. Departamento de Economía.
    14. 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.
    15. Martín González-Rozada & Luis Pereiro, 2013. "Forecasting Prices in Regime-Switching Markets," Department of Economics Working Papers 2013_2, Universidad Torcuato Di Tella.
    16. Shyh-Wei Chen & Chi-Sheng Hsu & Cyun-Jhen Pen, 2016. "Are Inflation Rates Mean-reverting Processes? Evidence from Six Asian Countries," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 12(1), pages 119-155, February.
    17. 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.

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    Keywords

    geometric ergodicity;

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