TY - JOUR
T1 - Correlation and the time interval over which the variables are measured
AU - Levy, Haim
AU - Schwarz, Gideon
PY - 1997
Y1 - 1997
N2 - When two random variables are multiplicative over time, their correlation coefficient is not invariant under changes of the differencing interval even when each of the random variables is a product of i.i.d. variables over time. It is shown that unless Y = kX, k > 0, the coefficient of determination (ρ2) decreases monotonically as the differencing interval increases, approaching zero in the limit. In sampling for empirical studies, the differencing interval is often selected arbitrarily. Such a choice may dramatically affect the sample correlation coefficient, as well as its statistical significance.
AB - When two random variables are multiplicative over time, their correlation coefficient is not invariant under changes of the differencing interval even when each of the random variables is a product of i.i.d. variables over time. It is shown that unless Y = kX, k > 0, the coefficient of determination (ρ2) decreases monotonically as the differencing interval increases, approaching zero in the limit. In sampling for empirical studies, the differencing interval is often selected arbitrarily. Such a choice may dramatically affect the sample correlation coefficient, as well as its statistical significance.
KW - Correlation coefficient
KW - Differencing interval
KW - Investment horizon
KW - Stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=0008612030&partnerID=8YFLogxK
U2 - 10.1016/0304-4076(95)01795-X
DO - 10.1016/0304-4076(95)01795-X
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AN - SCOPUS:0008612030
SN - 0304-4076
VL - 76
SP - 341
EP - 350
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1-2
ER -