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The ACR model: a multivariate dynamic mixture autoregression

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Author Info
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)

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Abstract

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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Keywords: Dynamic mixture vector autoregressive mmodel; autoregressive conditional root model; ACR; regime switching; stochastic unit root; threshold autoregression;

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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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