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An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application

Author

Listed:
  • Takamitsu Kurita

    (Faculty of Economics, Fukuoka University)

  • Heino Bohn Nielsen

    (Department of Economics, University of Copenhagen)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen and CREATES)

Abstract

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.

Suggested Citation

  • Takamitsu Kurita & Heino Bohn Nielsen & Anders Rahbek, 2009. "An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application," CREATES Research Papers 2009-28, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-28
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    References listed on IDEAS

    as
    1. Diamandis, Panayiotis F. & Georgoutsos, Dimitris A. & Kouretas, Georgios P., 2000. "The monetary model in the presence of I(2) components: long-run relationships, short-run dynamics and forecasting of the Greek drachma," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 917-941, December.
    2. Juselius, Katarina, 1998. "A Structured VAR for Denmark under Changing Monetary Regimes," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 400-411, October.
    3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    4. Palumbo, Michael & Rudd, Jeremy & Whelan, Karl, 2006. "On the Relationships Between Real Consumption, Income, and Wealth," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 1-11, January.
    5. Heino Nielsen & Christopher Bowdler, 2006. "Inflation adjustment in the open economy: an I(2) analysis of UK prices," Empirical Economics, Springer, vol. 31(3), pages 569-586, September.
    6. Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, vol. 124(2), pages 205-225, February.
    7. Luca Fanelli & Emanuele Bacchiocchi, 2005. "Testing the purchasing power parity through I(2) cointegration techniques," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 749-770.
    8. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
    9. Jurgen A. Doornik, 1998. "Approximations To The Asymptotic Distributions Of Cointegration Tests," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 573-593, December.
    10. Paruolo, Paolo, 2000. "Asymptotic Efficiency Of The Two Stage Estimator In I (2) Systems," Econometric Theory, Cambridge University Press, vol. 16(4), pages 524-550, August.
    11. Nielsen, Heino Bohn, 2002. "An I(2) Cointegration Analysis of Price and Quantity Formation in Danish Manufactured Exports," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(5), pages 449-472, December.
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    More about this item

    Keywords

    Cointegration; I(2); Piecewise linear trends; Likelihood analysis; US consumption;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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