Long Memory and Aggregation in Macroeconomic Time Series

This paper explores the interaction between long memory and aggregation. Results are derived which link the (possibly fractional) orders of integration of the aggregate series with those of the underlying series when the aggregation is either cross-sectional or temporal (in discrete or continuous time). These results provide empirically testable hypotheses which are examined using six U.K. macroeconomic series. A semiparametric method is found to be broadly consistent with the implications of the theory, but fully parametric ARFIMA models show considerable variation. Each series appears to be integrated of an order of between one and one-and-a-half.