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The ACR Model: A Multivariate Dynamic Mixture Autoregression

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  • Frédérique Bec
  • Anders Rahbek
  • Neil Shephard

Abstract

This paper proposes and analyses the autoregressive conditional root (ACR) time-series model. This multivariate dynamic mixture autoregression allows for non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2008.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1468-0084.2008.00512.x
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Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 70 (2008)
Issue (Month): 5 (October)
Pages: 583-618

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Handle: RePEc:bla:obuest:v:70:y:2008:i:5:p:583-618
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Cited by:

  1. Anders Rahbek & Heino Bohn Nielsen, 2012. "Unit Root Vector Autoregression with volatility Induced Stationarity," CREATES Research Papers 2012-29, School of Economics and Management, University of Aarhus.
  2. Dueker, Michael J. & Psaradakis, Zacharias & Sola, Martin & Spagnolo, Fabio, 2011. "Multivariate contemporaneous-threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 160(2), pages 311-325, February.
  3. Koop, Gary & Potter, Simon, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Journal of Econometrics, Elsevier, vol. 159(1), pages 134-150, November.
  4. Daiki Maki, 2013. "Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications," Empirical Economics, Springer, vol. 45(1), pages 605-625, August.
  5. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
  6. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, vol. 172(1), pages 1-13.
  7. Søren Johansen & Theis Lange, 2011. "Some Econometric Results for the Blanchard-Watson Bubble Model," Discussion Papers 11-15, University of Copenhagen. Department of Economics.

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