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

PLoS One. 2018 Nov 8;13(11):e0206929. doi: 10.1371/journal.pone.0206929. eCollection 2018.

Abstract

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 (ρ) between variables (often asset returns) and that ρ 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 ρ increases with n and that r does not share this disadvantage. Therefore, we suggest using Spearman when one (or both) variable is multiplicative.

MeSH terms

  • Data Interpretation, Statistical*
  • Humans
  • Normal Distribution*
  • Sample Size
  • Social Sciences / methods*

Grants and funding

The authors received no specific funding for this work.