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

Author

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  • Haim Levy

    (School of Business, Hebrew University of Jerusalem, Mount Scopus 91905, Jerusalem, Israel)

  • Ilan Guttman

    (School of Business, Hebrew University of Jerusalem, Mount Scopus 91905, Jerusalem, Israel)

  • Isabel Tkatch

    (School of Business, Hebrew University of Jerusalem, Mount Scopus 91905, Jerusalem, Israel)

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 (\rho 2 n ) 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 \rho 2 n 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.

Suggested Citation

  • Haim Levy & Ilan Guttman & Isabel Tkatch, 2001. "Regression, Correlation, and the Time Interval: Additive-Multiplicative Framework," Management Science, INFORMS, vol. 47(8), pages 1150-1159, August.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:8:p:1150-1159
    DOI: 10.1287/mnsc.47.8.1150.10225
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    References listed on IDEAS

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    Cited by:

    1. R Jea & C-T Su & J-L Lin, 2005. "Time aggregation effect on the correlation coefficient: added-systematically sampled framework," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(11), pages 1303-1309, November.
    2. Moshe Levy, 2012. "On the Spurious Correlation Between Sample Betas and Mean Returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(4), pages 341-360, September.
    3. Jea, Rong & Lin, Jin-Lung & Su, Chao-Ton, 2005. "Correlation and the time interval in multiple regression models," European Journal of Operational Research, Elsevier, vol. 162(2), pages 433-441, April.
    4. Pankaj Agrrawal & Faye W. Gilbert & Jason Harkins, 2022. "Time Dependence of CAPM Betas on the Choice of Interval Frequency and Return Timeframes: Is There an Optimum?," JRFM, MDPI, vol. 15(11), pages 1-18, November.
    5. Shlomo Yitzhaki & Peter Lambert, 2014. "Is higher variance necessarily bad for investment?," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 855-860, November.
    6. Edna Schechtman & Amit Shelef, 2018. "Correlation and the time interval over which the variables are measured – A non-parametric approach," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-9, November.

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