Correlation and the time interval over which the variables are measured - A non-parametric approach

It is known that when one (or both) variable is multiplicative, the choice of differencing intervals (n) (for example, differencing interval of n = 7 means a weekly datum which is the product of seven daily data) affects the Pearson correlation coefficient (rho) between variables (often asset returns) and that rho converges to zero as n increases. This fact can cause the resulting correlation to be arbitrary, hence unreliable. We suggest using Spearman correlation (r) and prove that as n increases Spearman correlation tends to a limit which only depends on Pearson correlation based on the original data (i.e., the value for a single period). In addition, we show, via simulation, that the relative variability (CV) of the estimator of rho increases with n and that r does not share this disadvantage. Therefore, we suggest using Spearman when one (or both) variable is multiplicative.