Testing for Normality in Weak Dependent Time Series

Abstract

Many statistical procedures rely on the assumption of normality in the dataset being analyzed. However, many of the standard tests for normality assume independent observations. In this thesis, we look at two methods proposed to test for normality of weakly dependent data, typically time series. The bootstrap-based Anderson-Darling test (BAD) has been proposed as a powerful method to test normality in univariate data, while a technique combining information from skewness, kurtosis, and correlation has been proposed as a method to test multivariate normality in time series. In this thesis, we use simulated data to estimate Type I and Type II error rates for these methods, and compare the results with those of several ”standard” methods that assume independence. We also apply these methods to several real datasets to assess their normality.