This paper used cross-sectional aggregation as the inspiration for a model with long-range dependence that arises in actual data. One of the advantages of our model is that it is less brittle than fractionally integrated processes. In particular, we showed that the antipersistent phenomenon is not present for the crosssectionally aggregated process. We proved that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for nonfractional long-range-dependent processes with negative degrees of persistence. As an application, we showed how we can approximate a fractionally differenced process using theoretically-motivated cross-sectional aggregated long-range-dependent processes. An example with temperature data showed that our framework provides a better fit to the data than the fractional difference operator.