Using OLS to Test for Normality

16 Pages Posted: 19 Jul 2012  

Haim Shalit

Ben-Gurion University of the Negev - Department of Economics

Date Written: July 14, 2012

Abstract

Yitzhaki (1996) showed that the OLS estimator of the slope coefficient in a simple regression is a weighted average of the slopes delineated by adjacent observations. The weights depend only on the distribution of the independent variable. In this paper I demonstrate that equal weights can only be obtained if and only if the independent variable is normally distributed. This necessary and sufficient condition is used to develop a new test for normality which is distribution free and not sensitive to outliers. The test is compared with standard normality tests, in particular, the popular Jarque-Bera test. It is shown that the new test provides a better power for testing normality against all classes of alternative distributions. Finally, the test is applied to check normality in time-series data from major international financial markets.

Keywords: regression weights, Jarque-Bera test, Kolmogorov-Smirnov test

JEL Classification: C10

Suggested Citation

Shalit, Haim, Using OLS to Test for Normality (July 14, 2012). Available at SSRN: https://ssrn.com/abstract=2111936 or http://dx.doi.org/10.2139/ssrn.2111936

Haim Shalit (Contact Author)

Ben-Gurion University of the Negev - Department of Economics ( email )

Department of Economics
Beer-Sheva 84105
Israel
+972-8-6472299 (Phone)
+972-8-6472941 (Fax)

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