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The ACR Model: A Multivariate Dynamic Mixture Autoregression

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Author Info
Frédérique Bec
Anders Rahbek
Neil Shephard

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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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  1. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115. [Downloadable!] (restricted)
  2. Sercu, Piet & Uppal, Raman & Van Hulle, Cynthia, 1995. " The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Purchasing Power Parity," Journal of Finance, American Finance Association, vol. 50(4), pages 1309-19, September. [Downloadable!] (restricted)
  3. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July. [Downloadable!] (restricted)
  4. Wong C.S. & Li W.K., 2001. "On a Mixture Autoregressive Conditional Heteroscedastic Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 982-995, September. [Downloadable!] (restricted)
  5. Zhiqiang Zhang & Wai Keung Li & Kam Chuen Yuen, 2006. "On a Mixture GARCH Time-Series Model," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(4), pages 577-597, 07. [Downloadable!] (restricted)
  6. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September. [Downloadable!] (restricted)
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  1. Michael Dueker & Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2009. "Multivariate Contemporaneous Threshold Autoregressive Models," Department of Economics Working Papers 2009-03, Universidad Torcuato Di Tella. [Downloadable!]
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