Regression, Correlation, and the Time Interval: Additive-Multiplicative Framework

Management Science, Vol. 47, No. 8, pp. 1150-1159, August 2001

10 Pages Posted: 14 Jul 2007

See all articles by Haim Levy

Haim Levy

Hebrew University of Jerusalem - Jerusalem School of Business Administration; Fordham University

Ilan Guttman

Leonard N. Stern School of Business, New York University; New York University - Stern Scholl of business

Isabel Tkatch

Georgia State University - J. Mack Robinson College of Business

Abstract

When two random variables are both additive or multiplicative, the effect of the way one "slices" the available period to subperiods (time intervals) is well documented in the literature. In this paper, we investigate the time interval effect when one of the variables is additive and one is multiplicative. We prove that the squared multiperiod correlation coefficient (ρ2n) decreases monotonically as n increases, and approaches zero when n goes to infinity. However, for relevant data corresponding to the U.S. stock market index, when shifting from weekly parameters to quarterly parameters the decrease in (ρ2n) is negligible. The effect on the regression coefficient is much more dramatic and even a shift from weekly data to quarterly data affects the regression coefficient substantially. The regression slope generally approaches zero, minus infinity or plus infinity, as the number of periods increases. Montonicity, however, exists only in certain cases.

Keywords: Correlation Coefficient, Regression Coefficient (Beta), Time Interval

Suggested Citation

Levy, Haim and Guttman, Ilan and Tkatch, Isabel, Regression, Correlation, and the Time Interval: Additive-Multiplicative Framework. Available at SSRN: https://ssrn.com/abstract=1000664

Haim Levy (Contact Author)

Hebrew University of Jerusalem - Jerusalem School of Business Administration ( email )

Mount Scopus
Jerusalem, 91905
Israel

HOME PAGE: http://pluto.huji.ac.il/~mshlevy/

Fordham University ( email )

140 West 62nd Street
New York, NY 10023
United States

Ilan Guttman

Leonard N. Stern School of Business, New York University ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

New York University - Stern Scholl of business ( email )

No Address Available

Isabel Tkatch

Georgia State University - J. Mack Robinson College of Business ( email )

P.O. Box 4050
Atlanta, GA 30303-3083
United States

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