The ACR Model: A Multivariate Dynamic Mixture Autoregression

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Frederique Bec, Anders Christian Rahbek, Neil Shephard

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.
Original languageEnglish
JournalOxford Bulletin of Economics and Statistics
Volume70
Issue number5
Pages (from-to)583-618
Number of pages35
ISSN0305-9049
DOIs
Publication statusPublished - 2008

ID: 10157337