Using OLS to Test for Normality

Haim Shalit
2012 Social Science Research Network  
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 characteristic is used to develop a new test for normality which is distribution free and not sensitive to outliers. The
more » ... est is compared with standard normality tests, in particular, the popular Jarque-Bera test. It is shown that the new test is 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.
doi:10.2139/ssrn.2111936 fatcat:5z2qaeye6bfflhhqridnh5f27y