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.
- 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).
- 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:
- Silvapulle & Podivinsky "The effect of non-normal disturbances and conditional heteroskedasticity on multiple cointegration tests" (2000)
- Johansen "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model" (2002)
- Hubrich et al. "A Review of Systems Cointegration Tests" (2001)
- Cheung & Lai "Finite‐sample sizes of Johansen's likelihood ratio tests for cointegration" (1993)
- 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.