TY - JOUR

T1 - Correlation and the time interval over which the variables are measured – A nonparametric approach

AU - Schechtman, Edna

AU - Shelef, Amit

N1 - Publisher Copyright:
© 2018 Schechtman, Shelef. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85056339865&partnerID=8YFLogxK

U2 - 10.1371/journal.pone.0206929

DO - 10.1371/journal.pone.0206929

M3 - Article

C2 - 30408091

AN - SCOPUS:85056339865

SN - 1932-6203

VL - 13

JO - PLoS ONE

JF - PLoS ONE

IS - 11

M1 - e0206929

ER -