Abstract
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.
Acknowledgement
We thank participants, an anonymous referee and Mehdi Hosseinkouchack for helpful comments, and are very grateful to Kung-Sik Chan for correcting the proof of Proposition 1. The first author carried out this research within the project HA 3306/5-1 financed by the German Research Foundation (DFG), while the second author thanks Academia Sinica and the National Science Council of the Republic of China (NSC 98-2118-M-001-023-MY2) for support. Finally, we wish to thank the Editor-in-Chief, Javier Hidalgo, for helping us with the manuscript.
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An earlier version of this paper was presented at the Joint Meeting of the 2011 Taipei International Statistical Symposium and the 7th Conference of the Asian Regional Section of the IASC.
©2013 by Walter de Gruyter Berlin / Boston