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Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model

Author

Listed:
  • H. Peter Boswijk

    (University of Amsterdam)

  • Michael Jansson

    (UC Berkeley)

  • Morten Ø. Nielsen

    (Queen's University)

Abstract

This discussion paper resulted in a publication in the 'Journal of Econometrics' , 2015, 184(1), 97-110. 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 of course the asymptotic results apply more generally. The power gains relative to existing tests are due to two factors. 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, Rothenberg, and Stock (1996). Secondly, 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

  • H. Peter Boswijk & Michael Jansson & Morten Ø. Nielsen, 2012. "Improved Likelihood Ratio Tests for Cointegration Rank in the VAR Model," Tinbergen Institute Discussion Papers 12-097/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20120097
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    References listed on IDEAS

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    Cited by:

    1. Liang, Chong & Schienle, Melanie, 2019. "Determination of vector error correction models in high dimensions," Journal of Econometrics, Elsevier, vol. 208(2), pages 418-441.
    2. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Other publications TiSEM bc68a2f2-3ca3-443c-b3ac-f, Tilburg University, School of Economics and Management.
    3. Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    4. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    5. Samuel Brien & Michael Jansson & Morten Ørregaard Nielsen, 2022. "Nearly Efficient Likelihood Ratio Tests of a Unit Root in an Autoregressive Model of Arbitrary Order," Working Paper 1429, Economics Department, Queen's University.
    6. 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.
    7. 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," Other publications TiSEM d1b040c9-db57-4e55-846f-4, Tilburg University, School of Economics and Management.
    8. Al-Sadoon, Majid M., 2017. "A unifying theory of tests of rank," Journal of Econometrics, Elsevier, vol. 199(1), pages 49-62.
    9. 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.

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    More about this item

    Keywords

    Cointegration rank; efficiency; likelihood ratio test; vector autoregression;
    All these keywords.

    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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