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Finite Sample Lag Adjusted Critical Values of the ADF-GLS Test

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Abstract

Ng and Perron (Econometrica 69:1519–1554, 2001) demonstrated the merits to employing their Modified Akaike Information Criterion to select the optimal lag length in the Elliott, Rothenberg and Stock (Econometrica 64:813–836, 1996) unit rot test. Perron and Qu (Econ Lett 84:12–19, 2007) introduced an empirical method that resolved an associated power problem for non-local alternatives. While Cheung and Lai (Oxford Bull Econ Stat 57:411-419, 1995) contains response surface estimates to generate finite-sample, lag-adjusted critical five and ten percent values for use in applied work, these relate to the original Elliott et al. (Econometrica 64:813–836, 1996) test. This paper provides response surfaces estimates of critical values for both the Ng and Perron (Econometrica 69:1519–1554, 2001) and Perron and Qu (Econ Lett 84:12–19, 2007) approaches, demonstrating they are sometimes quite different, an important consideration when performing inference.

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Data and Computer Code Availability

Matlab programs to replicate the analysis and calculate finite sample lag adjusted critical values and probability values are available as electronic supplementary material and also at http://web.business.queensu.ca/faculty/psephton under MatlabFiles (ADFGLS2020.zip) and on request to the author (Peter.Sephton@queensu.ca).

Notes

  1. For example, GRETL allows one to perform both the Ng and Perron (2001) and Perron and Qu (2007) versions of the test.

  2. A simple Google Scholar search of the Cheung and Lai (1995) paper returned 427 citations in late September 2020.

  3. Otero and Baum (2017) provide response surface estimates of critical values without incorporating the adjustments suggested by Perron and Qu (2007), and they do not employ the Schwert (1989) approach to setting the maximum lag length.

  4. For present purposes the maximum lag will be set as kmax = int{12(T/100)25} where T is the total sample size and int{} refers to “the integer part of”.

  5. See Seo (2005).

  6. Equation (4) was also used to construct approximate probability values for the test following MacKinnon (1994, 1996). The supplementary Matlab programs calculate these approximate probability values for quantiles between 0.005 and 0.9995.

References

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  1. Smith School of Business, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Peter S. Sephton

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Sephton, P.S. Finite Sample Lag Adjusted Critical Values of the ADF-GLS Test. Comput Econ 59, 177–183 (2022). https://doi.org/10.1007/s10614-020-10082-6

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  • DOI: https://doi.org/10.1007/s10614-020-10082-6

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