# Cumulative returns are more correlated than non-cumulative

I was just comparing two daily returns series and noted that the correlation between them is a lot higher if they are cumulated (about .95 for cumulative returns, vs .15 for non-cumulative). I feel that there should be a simple intuitive explanation for why that is. Is it because these returns behave more similarly over longer time horizons? As opposed to day-to-day?

More generally, is it customary to look at the correlation of cumulative, or non-cumulative returns? What time horizons are used? For example, I have heard this rule of thumb that if the correlation is above 0.7, it means that the returns are highly correlated. But I feel that to be meaningful statements like that should also specify the type of the return and the time horizon.

How do you judge correlation between return series? What time horizons and return types do you use? What is highly correlated, or uncorrelated for you?

• The cumulated or integrated returns are non-stationary random variables and therefore the correlations are biased and unreliable ("spurious") and you should not use them according to modern Econometrics. cowles.yale.edu/sites/default/files/files/pub/d07/d0757.pdf Jul 3, 2020 at 3:36
• Hey. That make sense. But what about prices? Prices are also cumulated in a way. Is it customary to transform them to become non-stationary before analyzing correlations? Thank you so much for the link to the paper, btw. I will read it right now. Jul 3, 2020 at 3:47
• your first question was about returns. Returns are transformations of prices. Returns are computed from prices by taking the log-differences of prices in sequence. Prices are non-stationary and are transformed into stationary returns by doing the log-differencing. you do not transform prices to become non-stationary when prices already are non-stationary. The other guy said cumulative returns are non-stationary, whereas the regular returns are stationary Jul 13, 2020 at 2:23