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Journal of Time Series Econometrics

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Asymptotic Behavior of Temporal Aggregates in the Frequency Domain

Uwe Hassler
  • Corresponding author
  • Email:
/ Henghsiu Tsai
  • 1Goethe University Frankfurt, RuW, Grueneburgplatz 1, D-60323 Frankfurt, Germany
  • 2Academia Sinica, Institute of Statistical Science, Taipei 11529, Taiwan
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Published Online: 2013-05-15 | DOI: https://doi.org/10.1515/jtse-2012-0029


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.

Keywords: normalized spectral density; normalized spectral density; cumulation of time series; difference stationarity; long memory


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About the article

Published Online: 2013-05-15

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.

Citation Information: Journal of Time Series Econometrics, ISSN (Online) 1941-1928, ISSN (Print) 2194-6507, DOI: https://doi.org/10.1515/jtse-2012-0029. Export Citation

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Uwe Hassler
Journal of Time Series Analysis, 2013, Volume 34, Number 5, Page 562

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