Lags used in Variance Ratio Tests

[Beck55]

Hi there,

I'm currently running some variance ratio testes for my dissertation (Lo&MacKinlay, Wright) but I'm having trouble deciding with which lags I should choose for these testes.
I'm using daily, weekly and monthly data. In many of the papers I read it's used lags q = 2, 4, 8, 16. To me this makes sense if we're working with weekly data (2->one week, 4->one month...).
But if I'm working with daily data makes more sense choosing the lags q = 2, 5, 10, 20 (2->one day, 5->one week, 10->2 weeks, 20->one month).
For daily data should I use the standard q = 2, 4, 8, 16 or q = 2, 5, 10, 20?
Is it ok to use different lags for different kinds of data (daily, weekly, monthly) within the same study?

Thank you.