We have aggregated 12 weeks of data from 60 participants resulting in 1 number per week ( i.e., 12 observations total). We would like to know if it is possible to run a Granger Causality test on only 12 time points and specify a lag of 1. My guess is that since Granger Causality is based on regression, we need a sample size of at least 30. Thank you!
Technically it is possible to run the test using few observations. However, your sample size comes with two problems:
a) The obvious one is that few observations cause high uncertainty in your estimates (i.e. large standard errors, etc.). You might thus fail to reject the Null of "no Granger causality" due to the lack of power. Thus, if running the test you have to be careful to not misinterpret "absence of evidence" as "evidence of absence".
b) In dynamic models (unlike cross sectional studies) the OLS results are biased. You thus should use some kind of finite sample correction. The most simple one would be a straightforward bootstrap bias correction (such as Runkle in JBES 1987). A more sophisticated bias correction has recently been proposed by Bauer, Rudebusch and Wu in JBES 2012.
Long story short. If you can reject with a proper bias corrected estimator, you can safely reject noncausality. If you find nothing, you pretty much have evidence because failing to reject in such a small sample is not very informative.
Best
Makram
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