Persistence under temporal aggregation and differencing

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.