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Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles

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  • Massimo Franchi

    (Department of Statistical Sciences, Sapienza University of Rome, P.le A. Moro 5, 00198 Rome, Italy)

  • Søren Johansen

    (Department of Economics, University of Copenhagen, Øster Farimagsgade 5 Building 26, 1353 Copenhagen K, Denmark
    CREATES, Department of Economics and Business, Aarhus University, Building 1322, DK-8000 Aarhus C, Denmark)

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 multiple near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then two critical value adjustments suggested by McCloskey (2017) for the test on the cointegrating relations are implemented for the model with a single near unit root, and it is found by simulation that they eliminate the serious size distortions, with a 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," Econometrics, MDPI, vol. 5(2), pages 1-20, June.
    • Handle: RePEc:gam:jecnmx:v:5:y:2017:i:2:p:25-:d:101429
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    References listed on IDEAS

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    1. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    2. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    3. 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.
    4. 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.
    5. 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.
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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. 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.
    3. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    4. 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).
    5. 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.

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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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