Testing regression disturbances for normality with stable alternatives: further monte carlo evidence

Abstract

This paper extends previous Monte Carlo work on testing for normality of ordinary least squares regression residuals. In addition to considering variation in sample size, this study also considers the affects of variation in the number of regressors and misspecifying the degree of serial correlation in the population residuals. Based on simulations using stably distributed alternatives with varying degrees of skewness, evidence is provided that: increasing the column dimension of the matrix of exogenous variables leads to a reduction in the power of parametric normality tests in small samples; and, misspecification of the degree of serial correlation has a significant affect on parametric normality test results, across all sample sizes.

Keywords:

• Normality testing
• Monte Carlo study
• stable distributions
• serial correlation
• projec-tion matrix
• simulation

^∗The author would like to thank Peter Kennedy and the referee for useful comments. Ken Kingsbury and Nanda Kumar-Stenger provided computer assistance.

^∗The author would like to thank Peter Kennedy and the referee for useful comments. Ken Kingsbury and Nanda Kumar-Stenger provided computer assistance.

Notes

^∗The author would like to thank Peter Kennedy and the referee for useful comments. Ken Kingsbury and Nanda Kumar-Stenger provided computer assistance.