Asymptotic Behavior of Temporal Aggregates in the Frequency Domain

The classical aggregation result by Tiao (1972, Asymptotic Behavior of Temporal Aggregates of Time Series, Biometrika 59, 525–531) is generalized for a weak set of assumptions. The innovations driving the integrated processes are only required to be stationary with integrable spectral density. The derivation is settled in the frequency domain. In case of fractional integration, it is demonstrated that the order of integration is preserved with growing aggregation under the same set of assumptions.