i have seen papers that study the statistical significance of the one versus the other. so that is one perspective. for bond markets it is yields versus returns, etc, so this is not really unique or isolated.

i am not sure whether it is possible to consistently argue the one is better than the other. both come with assumptions and use cases.

for example, prices may be more volatile than returns. prices may include speculative effects. it depends on the statistical premises your method assumes or relies on.

Dear Mohanned

I believe the log transformation is to make the distribution more normal as that is one of the assumptions when using OLS regression. As far as which to use, prices or returns, I would choose what you want to explain. Otherwise, your discussion of results may be awkward. That is, if you want to explain the price effects but chose return the coefficient would not be directly empirically interpretable.

Dear Brian, Raymond, and, Thoma.

Thank you for your contribution and your answers helped me to avoid any confusion.

Kind regards,

I agree with Thomas Dimpfl. It is quite important to ascertain the salient statistical features inherent in the data before embarking on any time series estimation.

Dear Ahamuefula,

Yes I agree with you and Thomas because before asking I tested the stationarty for both price and return by ADF and PP and also by the graph it seems to me the return is better than price but I got confused when some scholars used the price instead of returns.

Thomas and others make it very clear now.

Thank you all!

kind regards

Log differences are typically used to calculate compound financial returns.

It is not mathematically possible for both prices and log prices to be I(1), although both can be I(0).

If price is I(1), then the first difference in prices will be I(0), as will be the simple rate of returns.

If lop price is I(1), then the log differences in prices will be I(0).