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There is a wide availability of methods for testing normality under theassumption of independent and identically distributed data. When data aredependent in space and/or time, however, assessing and testing the marginalbehavior is considerably more challenging, as the marginal behavior is impactedby the degree of dependence. We propose a new approach to assess normality fordependent data by non-linearly incorporating existing statistics from normalitytests as well as sample moments such as skewness and kurtosis through a neuralnetwork. We calibrate (deep) neural networks by simulated normal and non-normaldata with a wide range of dependence structures and we determine theprobability of rejecting the null hypothesis. We compare several approaches fornormality tests and demonstrate the superiority of our method in terms ofstatistical power through an extensive simulation study. A real worldapplication to global temperature data further demonstrates how the degree ofspatio-temporal aggregation affects the marginal normality in the data.

A Neural Network-Based Approach to Normality Testing for Dependent Data