Open AccessCorrelation and the time interval over which the variables are measured – A non-parametric approach
Author(s) -
Edna Schechtman,
Amit Shelef
Publication year - 2018
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0206929
Subject(s) - statistics , spearman's rank correlation coefficient , mathematics , correlation , multiplicative function , estimator , correlation coefficient , nonparametric statistics , pearson product moment correlation coefficient , confidence interval , mathematical analysis , geometry
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.