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The ACR model: a multivariate dynamic mixture autoregression

  • Frédérique Bec

    ()

    (CREST-LMA, Timbre J360, 15 boulevard Gabriel Peri, 92245 Malakoff CEDEX and THEMA, University of Cergy-Pontoise, France)

  • Anders Rahbek

    ()

    (Department of Economics, University of Copenhagen and Studiestraede 6, DK-1455 Copenhagen K, Denmark)

  • Neil Shephard

    ()

    (Oxford-Man Institute and Economics Department, University of Oxford and Blue Boar Court, Alfred Road, Oxford OX1 4EH, United-Kingdom)

In this paper we propose and analyse the Autoregressive Conditional Root (ACR) time series mmodel. It is a multivariate dynamic mixture autoregression which allows for non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models such as e.g. the threshold autoregressive or Markov switching classes of models, which are commonly used to describe non-linear 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, we establish consistency and asymptotic normality of the maximum likelihood estimators in the ACR model. An application to real exchange rate data illustrates the conclusions and analysis.

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Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2008-11.

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Date of creation: 2008
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Handle: RePEc:ema:worpap:2008-11
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