Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.10

Online
ISSN
1941-1928
See all formats and pricing
More options …

Asymptotic Behavior of Temporal Aggregates in the Frequency Domain

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

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.

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

References

  • Brewer, K. R. W. 1973. “Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX Models.” Journal of Econometrics, 1: 133–54.Google Scholar

  • Chambers, M. J. 1998. “Long Memory and Aggregation in Macroeconomic Time Series.” International Economic Review 39: 1053–72.CrossrefGoogle Scholar

  • Drost, F. C. 1994. “Temporal aggregation of time-series.” In Econometric Analysis of Financial Markets edited by J. Kachler and P. Kugler, 11–21. Heidelberg: Physica.Google Scholar

  • Gradshteyn, I. S., and I. M. Ryzhik. 2000. Tables of Integrals, Series, and Products. San Diego: Academic Press.Google Scholar

  • Granger, C. W. J., and R. Joyeux. 1980. “An Introduction to Long-Memory Time Series Models and Fractional Differencing.” Journal of Time Series Analysis 1: 15–29.Google Scholar

  • Hassler, U. 2011. “Estimation of Fractional Integration Under Temporal Aggregation.” Journal of Econometrics 162: 240–47.Web of ScienceGoogle Scholar

  • Hidalgo, J.2005. “Semiparametric Estimation for Stationary Processes Whose Spectra Have an Unknown Pole.” The Annals of Statistics 33: 1843–89.CrossrefGoogle Scholar

  • Hosking, J. R. M. 1981. “Fractional Differencing.” Biometrika, 68: 165–76.Google Scholar

  • Jolley, L. B. W. 1961. Summation of Series. New York: Dover Publications.Google Scholar

  • Lütkepohl, H. 1987. Forecasting Aggregated Vector ARMA Processes. Heidelberg: Springer.Google Scholar

  • Man, K. S., and Tiao, G. C. 2006. “Aggregation Effect and Forecasting Temporal Aggregates of Long Memory Process.” International Journal of Forecasting 22: 267–81.CrossrefGoogle Scholar

  • Marcellino, M. 1999. “Some Consequences of Temporal Aggregation in Empirical Analysis.” Journal of Business & Economic Statistics 17: 129–36.Google Scholar

  • Nelson, C. R., and C. I. Plosser. 1982. “Trends and Random Walks in Marcoeconomic Time Series: Some Evidence and Implications.” Journal of Monetary Economics 10: 139–62.CrossrefGoogle Scholar

  • Rossana, R. J., and J. J. Seater. 1995. “Temporal Aggregation and Economic Time Series.” Journal of Business & Economic Statistics 13: 441–51.Google Scholar

  • Samorodnitsky, G., and M. S. Taqqu. 1994. Stable Non-Gaussian Random Processes. New York: Chapman and Hall.Google Scholar

  • Silvestrini, A., and D. Veredas. 2008. “Temporal Aggregation of Univariate and Multivariate Time Series Models: A Survey.” Journal of Economic Surveys 22: 458–97.Web of ScienceCrossrefGoogle Scholar

  • Souza, L. R. 2005. “A Note on Chambers’s ‘Long Memory and Aggregation in Macroeconomic Time Series’”. International Economic Review 46: 1059–62.CrossrefGoogle Scholar

  • Stram, D. O., and W. W. S. Wei. 1986. “Temporal Aggregation in the ARIMA Process.” Journal of Time Series Analysis 7: 279–92.CrossrefGoogle Scholar

  • Tiao, G. C. 1972. “Asymptotic Behaviour of Temporal Aggregates of Time Series.” Biometrika 59: 525–31.CrossrefGoogle Scholar

  • Tsai, H., and K. S. Chan. 2005. “Temporal Aggregation of Stationary and Nonstationary Discrete-Time Processes.” Journal of Time Series Analysis 26: 613–24.CrossrefGoogle Scholar

  • Wei, W. W. S. 1990. Time Series Analysis: Univariate and Multivariate Methods. New York: Addison-Wesley.Google Scholar

  • Weiss, A. A. 1984. “Systematic Sampling and Temporal Aggragation in Time Series Models.” Journal of Econometrics 26: 271–82.CrossrefGoogle Scholar

  • Working, H. 1960. “A Note on the Correlation of First Differences of Averages in a Random Chain.” Econometrica 26: 916–18.CrossrefGoogle Scholar

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

©2013 by Walter de Gruyter Berlin / Boston. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Christian Schumacher
International Journal of Forecasting, 2016, Volume 32, Number 2, Page 257
[2]
Uwe Hassler
Journal of Time Series Analysis, 2013, Volume 34, Number 5, Page 562

Comments (0)

Please log in or register to comment.
Log in