Aggregation of the generalized fractional processes

•The spectrum of the generalized fractional process under aggregation is proposed.•Skip sampling might cause long memory at frequency zero.•Temporal aggregation does not induce long memory at frequency zero.•Simulation results are consistent with the theoretical findings.

The paper studies the interaction between aggregation and persistence pertaining to skip sampling of stock variables as well as temporal aggregation of flow variables for the generalized fractional processes. We show that, for skip sampling, the long memory feature at the zero frequency can arise from the aggregation of a generalized fractional series, while temporal aggregation does not induce such phenomenon. Simulation results are included to demonstrate the practical relevance of the theoretical results.