Persistence under temporal aggregation and differencing

•Cumulating•Skip sampling•Difference-stationarity•Seasonal differencing•Temporal aggregation

Temporal aggregation is known to affect the persistence of time series. We study the aggregation of flow variables as well as stock data, and difference-stationarity is allowed for. Moreover, moving averages encountered when computing annual growth rates (seasonal differences) are investigated. Using a relative persistence measure (long-run variance ratio), it is clarified when persistence is increased or decreased, and by how much. Our results are exact for a finite aggregation level. They are illustrated with monthly time series. Approximate results for the growing aggregation level are provided, too.