Regression, correlation, and the time interval: Additive-multiplicative framework

Then two random variables are both additive or multiplicative, the effect o f the way one "slices" the available period to subperiods (time intervals) is well documented in the literature. In this paper, we investigate the tim e interval effect when one of the variables is additive and one is multipli cative. We prove that the squared multiperiod correlation coefficient (rho (2)(n)) decreases monotonically as n increases, and approaches zero when n goes n to infinity. However, for relevant data corresponding to the U.S. st ock market index, when shifting from weekly parameters to quarterly paramet ers the decrease in rho (2)(n) is negligible. n The effect on the regressio n coefficient is much more dramatic and even a shift from weekly data to qu arterly data affects the regression coefficient substantially. The regressi on slope generally approaches zero, minus infinity or plus infinity, as the number of periods increases. Montonicity, however, exists only in certain cases.