It is commonly argued that observed long memory in time series and financial variables can result from cross-sectional aggregation of dynamic heterogeneous micro units. We demonstrate that the aggregation argument is consistent with a range of different long memory de?finitions. In a simulation study we show however that both the cross-section and time dimensions have to be rather large to reflect the true implied memory when using commonly used estimators, especially when the theoretical memory is not too high. Finally, we show that even though the aggregated process will converge to a fractional Brownian motion in the limit, the fractionally differenced series will still have an autocorrelation function that exhibits hyperbolic decay, but at a rate that still ensures summability. The fractionally differenced series is thus I(0) but standard ARFIMA modelling may be invalid when the long memory is caused by aggregation.