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The Use of Aggregate Time Series in Testing for Gaussianity

Many time series encountered in practice are non‐Gaussian. Because of the process of data collection or the practice or researchers, time series used in analysis and modelling are frequently temporal aggregates. In this paper, we study the effects of the use of aggregate time series on testing for Gaussianity. We analyse how the test statistic is affected by aggregation and how that affects the power of the test. The results show that the use of aggregate time series induces Gaussianity and that the degree of inducement increases with the order of aggregation. In fact, the use of aggregate time series reduces the power of the test, although the effect is not significant for low orders of aggregation.