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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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    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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