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The Autoregressive Conditional Root (ACR) Model

Author

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  • Frédérique Bec

    (Crest)

  • Anders Rahbek

    (Crest)

  • Neil Shephard

    (Crest)

Abstract

In this paper we propose and analyse the Autoregressive Conditional Root (ACR) timeseries model, which allows for endogenously generated regime switching between seemingly stationaryand non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models suchas e.g. the threshold autoregressive or Markov switching classes of models, which are commonly used todescribe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditionson the parameters of the ACR process and its innovations, are shown to imply geometric ergodicity,stationarity and existence of moments. Furthermore, we establish consistency and asymptotic normalityof the maximum likelihood estimators in the ACR model. An application to French-German exchangerate data illustrate the conclusions and analysis.

Suggested Citation

  • Frédérique Bec & Anders Rahbek & Neil Shephard, 2005. "The Autoregressive Conditional Root (ACR) Model," Working Papers 2005-26, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-26
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    Cited by:

    1. 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.
    2. Adusei Jumah & Robert M. Kunst, 2016. "Optimizing time-series forecasts for inflation and interest rates using simulation and model averaging," Applied Economics, Taylor & Francis Journals, vol. 48(45), pages 4366-4378, September.
    3. 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.

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