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I am looking for references regarding the behaviour of Johansen's cointegration test (trace test, perhaps also eigenvalue test) in small samples with non-normal innovations.

  1. I wonder how robust the test is to deviations from normality (which is mostly relevant in small samples but not so much asymptotically, if I understand it correctly).
  2. Also, I wonder whether Engle-Granger test could be preferred to the Johansen's test in small samples under any circumstances.

Something "light" like a textbook treatment would be preferred to technical articles. (I am not ready to dig very deep, but I need a citation for my research paper.)

The most relevant references I was able to find are the following:

  1. Silvapulle & Podivinsky "The effect of non-normal disturbances and conditional heteroskedasticity on multiple cointegration tests" (2000)
  2. Johansen "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model" (2002)
  3. Hubrich et al. "A Review of Systems Cointegration Tests" (2001)
  4. Cheung & Lai "Finite‐sample sizes of Johansen's likelihood ratio tests for cointegration" (1993)
  5. Gonzalo & Lee "On the robustness of cointegration tests when series are fractionally integrated" (2000)

Silvapulle & Podivinsky (2000) is quite relevant and quite readable, and basically answers my first question. Still, I wonder if there are more studies to confirm or contradict their findings.
Johansen (2002) is about small samples but not really about non-normality. Also, it is more about fixing the small sample problem rather examining the negative effects of the problem. Moreover, it is pretty technical and hard to digest.
Hubrich et al. (2001) examine a wide range of conditions but do not seem to provide overarching conclusions (perhaps they do not exist, though).
Cheung & Lai (1993) do not seem to discuss non-normality.
Gonzalo & Lee (2000) suggest that when the series are fractionally integrated rather than I(1), Engle-Granger test is preferred both in small samples and asymptotically to Johansen's test. So they answer my question number 2. I am still interested in other examples.

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  • $\begingroup$ I think the general conclusion is that its performance is quite terrible in small samples. A recent strand of papers have improved its performance using bootstrap methods, perhaps you'll find useful citations in these papers' introductions. For example, have a look at recent publications by Anders Rahbek. $\endgroup$ – hejseb Apr 9 '15 at 18:34
  • $\begingroup$ @hejseb, thanks for the idea! I will check these out. $\endgroup$ – Richard Hardy Apr 9 '15 at 18:43
  • $\begingroup$ Not a textbook treatment, I know, but perhaps this might be of interest as well taloustieteellinenyhdistys.fi/images/stories/fep/f1995_2d.pdf $\endgroup$ – hejseb Apr 9 '15 at 19:00

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