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Autoregressive conditional root model

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  • Neil Shephard
  • Anders Rahbek

Abstract

In this paper we develop a time series model which allows long-term disequilibriums to have epochs of non-stationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship. This autoregressive root model is shown to be ergodic and covariance stationary under some rather general conditions. We study how this model can be estimated and tested, developing appropriate asymptotic theory for this task. Finally we apply the model to assess the purchasing power parity relationship.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2002-W07.

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Date of creation: 01 Feb 2002
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Handle: RePEc:oxf:wpaper:2002-w07

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Related research

Keywords: Cointegration; Equilibrium correction model; GARCH; Hidden Markov model; Likelihood; Regime switching; STAR model; Stochastic break; Stochastic unit root; Switching regression; Real Exchange Rate; PPP; Unit root hypothesis;

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References

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  1. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  2. Paul A. Ruud., 1988. "Extensions of Estimation Methods Using the EM Algorithm.," Economics Working Papers, University of California at Berkeley 8899, University of California at Berkeley.
  3. Francis X. Diebold & Joon-Haeng Lee & Gretchen C. Weinbach, 1993. "Regime switching with time-varying transition probabilities," Working Papers 93-12, Federal Reserve Bank of Philadelphia.
  4. Durland, J Michael & McCurdy, Thomas H, 1994. "Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(3), pages 279-88, July.
  5. 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.
  6. Mark P. Taylor, 1995. "The Economics of Exchange Rates," Journal of Economic Literature, American Economic Association, vol. 33(1), pages 13-47, March.
  7. Christian Gourieroux & Christian Yann Robert, 2001. "Tails and Extremal Behaviour of Stochastic Unit Root Models," Working Papers, Centre de Recherche en Economie et Statistique 2001-28, Centre de Recherche en Economie et Statistique.
  8. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, Elsevier, vol. 64(1-2), pages 307-333.
  9. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1015, Cowles Foundation for Research in Economics, Yale University.
  10. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  11. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
  12. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 1(1), pages 3-15, March.
  13. 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., John Wiley & Sons, Ltd., vol. 14(2), pages 143-54, March-Apr.
  14. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 167-86, January.
  15. Granger, E.J. & Swanson, N.R., 1996. "An introduction to stochastic Unit Root Processes," Papers, Pennsylvania State - Department of Economics 4-96-3, Pennsylvania State - Department of Economics.
  16. 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, American Statistical Association, vol. 22, pages 382-395, October.
  17. 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, Iowa State University, Department of Economics 1388, Iowa State University, Department of Economics.
  18. Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
  19. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
  20. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, Elsevier, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  21. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 484-489, June.
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Citations

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Cited by:
  1. Jumah, Adusei & Kunst, Robert M., 2008. "Optimizing Time-series Forecasts for Inflation and Interest Rates Using Simulation and Model Averaging," Economics Series, Institute for Advanced Studies 231, Institute for Advanced Studies.
  2. Gary Koop & Simon Potter, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Post-Print, HAL hal-00732535, HAL.
  3. Angelos Kanas, 2009. "Real exchange rates and developing countries," International Journal of Finance & Economics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 14(3), pages 280-299.
  4. Kanas, Angelos, 2006. "Purchasing Power Parity and Markov Regime Switching," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 38(6), pages 1669-1687, September.
  5. Kaliva, Kasimir & Koskinen, Lasse, 2008. "Stock market bubbles, inflation and investment risk," International Review of Financial Analysis, Elsevier, Elsevier, vol. 17(3), pages 592-603, June.
  6. Gary Koop & Simon Potter, 2007. "A flexible approach to parametric inference in nonlinear time series models," Staff Reports, Federal Reserve Bank of New York 285, Federal Reserve Bank of New York.
  7. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, Elsevier, vol. 127(1), pages 69-81, July.
  8. Angelos Kanas, 2009. "Real exchange rate, stationarity, and economic fundamentals," Journal of Economics and Finance, Springer, Springer, vol. 33(4), pages 393-409, October.

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