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Improved likelihood ratio tests for cointegration rank in the VAR model

Author

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  • Boswijk, H. Peter
  • Jansson, Michael
  • Nielsen, Morten Ørregaard

Abstract

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.

Suggested Citation

  • Boswijk, H. Peter & Jansson, Michael & Nielsen, Morten Ørregaard, 2015. "Improved likelihood ratio tests for cointegration rank in the VAR model," Journal of Econometrics, Elsevier, vol. 184(1), pages 97-110.
  • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:97-110
    DOI: 10.1016/j.jeconom.2014.08.007
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    References listed on IDEAS

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    Cited by:

    1. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.
    2. repec:eee:econom:v:199:y:2017:i:1:p:49-62 is not listed on IDEAS
    3. Pierre Perron & Gabriel Rodríguez, "undated". "Residuals-based Tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series wp2015-017, Boston University - Department of Economics, revised 19 Oct 2015.
    4. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.
    5. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.

    More about this item

    Keywords

    Cointegration rank; Efficiency; Likelihood ratio test; Vector autoregression;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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