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An I(2) Cointegration Model With Piecewise Linear Trends: Likelihood Analysis And Application

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  • Takamitsu Kurita

    (Faculty of Economics, Fukuoka University)

  • Heino Bohn Nielsen

    (Department of Economics, University of Copenhagen)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

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.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 09-13.

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Length: 24 pages
Date of creation: Jul 2009
Date of revision:
Handle: RePEc:kud:kuiedp:0913

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Keywords: Cointegration; I(2); piecewise linear trends; likelihood analysis; US consumption;

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  1. 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.
  2. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  3. Palumbo, Michael & Rudd, Jeremy & Whelan, Karl, 2002. "On the Relationships Between Real Consumption, Income, and Wealth," Research Technical Papers 4/RT/02, Central Bank of Ireland.
  4. Heino Bohn Nielsen & Christopher Bowdler, 2003. "Inflation Adjustment in the Open Economy: An I(2) Analysis of UK Prices," Economics Papers 2003-W05, Economics Group, Nuffield College, University of Oxford.
  5. 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.
  6. 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.
  7. 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.
  8. Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, vol. 124(2), pages 205-225, February.
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