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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.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:obuest:v:70:y:2008:i:5:p:583-618
    DOI: 10.1111/j.1468-0084.2008.00512.x
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