Persistence under Temporal Aggregation and Differencing

Temporal aggregation is known to affect the persistence of time series, where persistence reflects, roughly speaking, the degree of positive serial correlation. It is suggested to measure persistence as percentage of the long-run variance not attributable to the variance ("long-run variance difference ratio"). Here we study the aggregation of flow variables as well as stock data, and difference-stationarity is allowed for. Moreover, moving averages encountered e.g. when computing annual growth rates (seasonal differences) are investigated. It is clarified when persistence is increased or decreased, and by how much. Our results are exact for finite aggregation level. They are illustrated with numerical examples and real data. Approximate results for growing aggregation level are provided, too