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Stochastic Unit Root Models

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  • Gourieroux, Christian
  • Robert, Christian Y.

Abstract

This paper develops a dynamic switching model, with a random walk and a stationary regime, where the time spent in the random walk regime is endogeneously predetermined. More precisely, we assume that the process is recursively defined by Yt = μ + Yt−1 + εt, with stochastic probability πrw(Yt−1), Yt = μ + εt, with stochastic probability 1 − πrw(Yt−1), where (εt) is a strong white noise and πrw is a nondecreasing function. Then, the dynamics of the process (Yt), its marginal distribution, and the distribution of the time spent in the unit root regime depend on the pattern of random walk intensity πrw and on the noise distribution F. Moreover, we study the links between the endogeneous switching regime and the degree of persistence of the process (Yt).

Suggested Citation

  • Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1052-1090, December.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1052-1090_06
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    Cited by:

    1. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
    2. Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, Department of Economics and Business Economics, Aarhus University.
    3. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    4. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    5. Anders Rahbek & Neil Shephard, 2001. "Autoregressive conditional root model," Economics Papers 2002-W7, Economics Group, Nuffield College, University of Oxford, revised 01 Feb 2002.
    6. Meitz, Mika & Saikkonen, Pentti, 2022. "Subgeometrically Ergodic Autoregressions," Econometric Theory, Cambridge University Press, vol. 38(5), pages 959-985, October.
    7. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    8. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
    9. Yin, Ming, 2015. "Estimating Gaussian Mixture Autoregressive model with Sequential Monte Carlo algorithm: A parallel GPU implementation," MPRA Paper 88111, University Library of Munich, Germany, revised 2018.
    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. Chin-Ping King, 2012. "Half Life of the Real Exchange Rate: Evidence from the Nonlinear Approach in Emerging Economies," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 8(1), pages 1-23, January.
    12. Rafal Kulik & Philippe Soulier, 2013. "Heavy tailed time series with extremal independence," Papers 1307.1501, arXiv.org, revised Oct 2014.
    13. P. Gagliardini & C. Gourieroux, 2008. "Duration time‐series models with proportional hazard," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 74-124, January.
    14. Frédérique Bec & Alain Guay & Heino Bohn Nielsen & Sarra Saïdi, 2022. "Power of unit root tests against nonlinear and noncausal alternatives," THEMA Working Papers 2022-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    15. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.

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