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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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2002/w7/acr.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2002-W7.

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Length: 30 pages
Date of creation: 01 Apr 2001
Date of revision: 01 Feb 2002
Handle: RePEc:nuf:econwp:0207

Contact details of provider:
Web page: http://www.nuff.ox.ac.uk/economics/

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.;

This paper has been announced in the following NEP Reports:

• NEP-ALL-2002-04-03 (All new papers)
• NEP-ECM-2002-04-06 (Econometrics)
• NEP-ETS-2002-04-03 (Econometric Time Series)
• NEP-IFN-2002-04-03 (International Finance)

References

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1. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
2. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
3. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
   
   • Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
   • 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.
   • Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
4. Gourieroux, Christian & Robert, Christian Y., 2006. "Stochastic Unit Root Models," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1052-1090, December.
5. Granger, E.J. & Swanson, N.R., 1996. "An introduction to stochastic Unit Root Processes," Papers 4-96-3, Pennsylvania State - Department of Economics.
   
   • Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
6. 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.
   
   • Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
   • Tom Doan, . "RATS programs to replicate Enders/Granger JBES(1998)on threshold unit roots," Statistical Software Components RTZ00054, Boston College Department of Economics.
7. 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.
8. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
   
   • Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
9. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
   
   • Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
10. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
11. 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.
12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
13. 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.
14. Mark P. Taylor, 1995. "The Economics of Exchange Rates," Journal of Economic Literature, American Economic Association, vol. 33(1), pages 13-47, March.
15. Christian Gourieroux & Christian Yann Robert, 2001. "Tails and Extremal Behaviour of Stochastic Unit Root Models," Working Papers 2001-28, Centre de Recherche en Economie et Statistique.
16. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
17. Engle, Robert F & Smith, Aaron, 1998. "Stochastic Permanent Breaks," University of California at San Diego, Economics Working Paper Series qt99v0s0zx, Department of Economics, UC San Diego.
    
    • 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.
18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
19. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.

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Citations

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Cited by:

1. Gary Koop & Simon Potter, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Post-Print peer-00732535, HAL.
   
   • 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.
2. Jumah, Adusei & Kunst, Robert M., 2008. "Optimizing Time-series Forecasts for Inflation and Interest Rates Using Simulation and Model Averaging," Economics Series 231, Institute for Advanced Studies.
3. Angelos Kanas, 2009. "Real exchange rates and developing countries," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 14(3), pages 280-299.
4. Angelos Kanas, 2009. "Real exchange rate, stationarity, and economic fundamentals," Journal of Economics and Finance, Springer, vol. 33(4), pages 393-409, October.
5. Gary Koop & Simon Potter, 2007. "A flexible approach to parametric inference in nonlinear time series models," Staff Reports 285, Federal Reserve Bank of New York.
6. Kaliva, Kasimir & Koskinen, Lasse, 2008. "Stock market bubbles, inflation and investment risk," International Review of Financial Analysis, Elsevier, vol. 17(3), pages 592-603, June.

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