Hi,

I am working on some data containing 1400 observations over a 7 year period, whereas the observations is for weekdays.

I am looking at historical price data on both Bitcoin and the S&P500 index, meaning I have 2 variables. I have understood that Pearsons correlation coefficient is the most common and that logarithmic returns is the most common for prices over time. We wish to find evidence that the two variables are uncorrelated over the 7 year period, and that the two variables are negatively correlated when examining sub-periods from the 7 year period.

While reading on the Internet I find that trustworthy economists say that the historical correlation between these two variables should be ´uncorrelated" (close to 0), which means from the start of Bitcoin being traded in higher volumes from 2013.

When doing a Pearson correlation coefficient in Stata, after generating logarithmic variables, for the whole period I find that the correlation is 0.580, statistically significant at a 5 % level. Meaning the value is way too high according to what economists say.

In contrast, when I am not using logarithmic variables I get that the Pearsons correlation coefficient is 0.041, which is a number I really wish to want. This coefficient is in contrast not statistically significant at any level.

So my question is, is it in this case wrong generating logarithmic variables in this case? Or am I better off eventually using another correlation method? Generally I am wondering if logarithmic returns is the right path for me here or not, also regarding what correlation coefficient to use.

Thank you in advance.

Tor Magne