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Improved inference on cointegrating vectors in the presence of a near unit root using adjusted quantiles

Author

Listed:
  • Massimo Franchi

    (Sapienza University of Rome)

  • Søren Johansen

    (University of Copenhagen and CREATES)

Abstract

It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper formulates a CVAR model allowing for many near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then a critical value adjustment suggested by McCloskey for the test on the cointegrating relations is implemented, and it is found by simulation that it eliminates size distortions and has reasonable power for moderate values of the near unit root parameter. The findings are illustrated with an analysis of a number of different bivariate DGPs.

Suggested Citation

  • Massimo Franchi & Søren Johansen, 2017. "Improved inference on cointegrating vectors in the presence of a near unit root using adjusted quantiles," CREATES Research Papers 2017-17, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2017-17
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    References listed on IDEAS

    as
    1. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    2. Francesca Di Iorio & Stefano Fachin & Riccardo Lucchetti, 2016. "Can you do the wrong thing and still be right? Hypothesis testing in I(2) and near-I(2) cointegrated VARs," Applied Economics, Taylor & Francis Journals, vol. 48(38), pages 3665-3678, August.
    3. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    4. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    5. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
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    Cited by:

    1. James A. Duffy & Jerome R. Simons, 2020. "Cointegration without Unit Roots," Papers 2002.08092, arXiv.org, revised Apr 2023.
    2. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    3. Cavusoglu, Nevin & Goldberg, Michael D. & Stillwagon, Josh, 2021. "Currency returns and downside risk: Debt, volatility, and the gap from benchmark values," Journal of Macroeconomics, Elsevier, vol. 68(C).
    4. Nevin Cavusoglu & Michael D. Goldberg & Joshua Stillwagon, 2019. "New Evidence on the Portfolio Balance Approach to Currency Returns," Working Papers Series 89, Institute for New Economic Thinking.
    5. Katarina Juselius, 2017. "Using a Theory-Consistent CVAR Scenario to Test an Exchange Rate Model Based on Imperfect Knowledge," Econometrics, MDPI, vol. 5(3), pages 1-20, July.

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    More about this item

    Keywords

    Long-run inference; test on cointegrating relations; likelihood inference; vector autoregressive model; near unit roots; Bonferroni type adjusted quantiles;
    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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