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The ACR model: a multivariate dynamic mixture autoregression

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  • 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)

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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Bibliographic Info

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. Paul A. Ruud., 1988. "Extensions of Estimation Methods Using the EM Algorithm.," Economics Working Papers 8899, University of California at Berkeley.
  2. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
  3. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
  4. Frederic Bec & Melika Ben Salem & Marine Carrasco, 2004. "Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 382-395, October.
  5. Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
    • Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
  6. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  7. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
  8. Maurice Obstfeld & Kenneth Rogoff, 2000. "The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?," NBER Working Papers 7777, National Bureau of Economic Research, Inc.
  9. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
  10. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
  11. Granger, E.J. & Swanson, N.R., 1996. "An introduction to stochastic Unit Root Processes," Papers 4-96-3, Pennsylvania State - Department of Economics.
  12. 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.
  13. Zhiqiang Zhang & Wai Keung Li & Kam Chuen Yuen, 2006. "On a Mixture GARCH Time-Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 577-597, 07.
  14. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  15. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-54, March-Apr.
  16. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
  17. Enders, Walter & Siklos, Pierre L, 2001. "Cointegration and Threshold Adjustment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 166-76, April.
  18. Berka, Martin, 2005. "General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence," MPRA Paper 234, University Library of Munich, Germany.
  19. Lutz Kilian & Mark P. Taylor, 2001. "Why is it so difficult to beat the Random Walk Forecast of Exchange Rates?," Tinbergen Institute Discussion Papers 01-031/4, Tinbergen Institute.
  20. 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.
  21. Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-84, November.
  22. Maurice Obstfeld & Alan M. Taylor, 1997. "Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher's Commodity Points Revisited," NBER Working Papers 6053, National Bureau of Economic Research, Inc.
  23. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
  24. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  25. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
  26. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-80.
  27. Jensen, S ren Tolver & Rahbek, Anders, 2007. "On The Law Of Large Numbers For (Geometrically) Ergodic Markov Chains," Econometric Theory, Cambridge University Press, vol. 23(04), pages 761-766, August.
  28. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
  29. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  30. Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
  31. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  32. 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.
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Citations

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Cited by:
  1. Anders Rahbek & Heino Bohn Nielsen, 2012. "Unit Root Vector Autoregression with volatility Induced Stationarity," CREATES Research Papers 2012-29, School of Economics and Management, University of Aarhus.
  2. Koop, Gary & Potter, Simon, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Journal of Econometrics, Elsevier, vol. 159(1), pages 134-150, November.
  3. Michael J. Dueker & Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2010. "Multivariate Contemporaneous-Threshold Autoregressive Models," UFAE and IAE Working Papers 817.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Søren Johansen & Theis Lange, 2011. "Some Econometric Results for the Blanchard-Watson Bubble Model," Discussion Papers 11-15, University of Copenhagen. Department of Economics.
  5. Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2013. "Estimation in threshold autoregressive models with a stationary and a unit root regime," Journal of Econometrics, Elsevier, vol. 172(1), pages 1-13.
  6. Daiki Maki, 2013. "Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications," Empirical Economics, Springer, vol. 45(1), pages 605-625, August.
  7. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.

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