Journal of Mathematics and Statistics

Statistical Size and Power of Eight Normality Tests in Presence of GARCH (1 1) Errors

Julio César Alonso and Daniela Estrada

DOI : 10.3844/jmssp.2019.12.21

Journal of Mathematics and Statistics

Volume 15, 2019

Pages 12-21


In this work, we assess the power and size of eight normality tests underthe assumption that errors follow a GARCH (1, 1) process by using MonteCarlo simulations. Four results stand out. First, the presence of a GARCH(1, 1) process increases the probability of making type I error. Second, Pearsonnormality test is recommended if it is assumed that errors follow a GARCH(1, 1) process. Third, statistical power varies depending on the type of heteroscedasticity and distribution considered. Fourth, normality tests have lowstatistical power and size (less than or equal to the nominal level) for smalland homoscedastic samples.


© 2019 Julio César Alonso and Daniela Estrada. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.