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Residuals‐based tests for the null of no‐cointegration: an Analytical comparison

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  • Elena Pesavento

Abstract

. This article studies the asymptotic distribution of five residuals‐based tests for the null of no‐cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares (GLS)‐detrended variables. The local asymptotic power of the tests is shown to be a function of Brownian motion and Ornstein–Uhlenbeck processes, depending on a single nuisance parameter, which is determined by the correlation at frequency zero of the errors of the cointegration regression with the shocks to the right‐hand side variables. The tests are compared in terms of power in large and small samples. It is shown that, while no significant improvement can be achieved by using unit root tests other than the OLS detrended t‐test originally proposed by Engle and Granger (1987), the power of GLS residuals tests can be higher than the power of system tests for some values of the nuisance parameter.

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  • Elena Pesavento, 2007. "Residuals‐based tests for the null of no‐cointegration: an Analytical comparison," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 111-137, January.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:1:p:111-137
    DOI: 10.1111/j.1467-9892.2006.00501.x
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    1. Neil R. Ericsson & James G. MacKinnon, 2002. "Distributions of error correction tests for cointegration," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 285-318, June.
    2. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    3. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
    4. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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    1. 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.
    2. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    3. Melo, Patricia C. & Sobreira, Nuno & Goulart, Pedro, 2019. "Estimating the long-run metro demand elasticities for Lisbon: A time-varying approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 126(C), pages 360-376.
    4. Tsen, Wong Hock, 2011. "The real exchange rate determination: An empirical investigation," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 800-811, October.
    5. Frederick Wallace, 2013. "Cointegration tests of purchasing power parity," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 149(4), pages 779-802, December.
    6. Karsten Reichold, 2022. "A Residuals-Based Nonparametric Variance Ratio Test for Cointegration," Papers 2211.06288, arXiv.org, revised Dec 2022.
    7. Gabriel Rodriguez & Pierre Perron, 2013. "Single-equation tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series 2013-016, Boston University - Department of Economics.

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