Robust testing for normality of error terms with presence of autocorrelation and conditional heteroscedasticity

Abstract

Normality of the error terms in regression models is one of the basic assumptions in the applied regression analysis. Therefore, testing for normality of the error terms constitutes one of the most important steps of regression model verification and validation. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Within the applied regression analysis there is a frequent problem of the presence of autocorrelation and conditional heteroscedasticity of the error terms. Under both autocorrelation and heteroscedasticity, the usual OLS estimators are still unbiased, linear and asymptotically normally distributed, however, no longer have the minimum variance property among all linear unbiased estimators.Therefore, the aim of this paper is to present and discuss normality testing of the error terms with presence of autocorrelation and conditional heteroscedasticity. To explore the power of selected classical tests and robust tests for normality, we perform simulation study.