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Tests for cointegration rank and the initial condition

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  • Niklas Ahlgren
  • Mikael Juselius

Abstract

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.
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  • Niklas Ahlgren & Mikael Juselius, 2012. "Tests for cointegration rank and the initial condition," Empirical Economics, Springer, vol. 42(3), pages 667-691, June.
    • Handle: RePEc:spr:empeco:v:42:y:2012:i:3:p:667-691
    DOI: 10.1007/s00181-010-0442-z
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    More about this item

    Keywords

    Asymptotic local power; Cointegration; Convergence; Initial condition; Likelihood ratio test; Unit root; C32;
    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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