IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v32y2005i4p583-597.html
   My bibliography  Save this article

Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes

Author

Listed:
  • HENGHSIU TSAI
  • K. S. CHAN

Abstract

. We study the autocorrelation structure of aggregates from a continuous‐time process. The underlying continuous‐time process or some of its higher derivative is assumed to be a stationary continuous‐time auto‐regressive fractionally integrated moving‐average (CARFIMA) process with Hurst parameter H. We derive closed‐form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. The limiting model of the aggregates, after appropriate number of differencing, is shown to be some functional of the standard fractional Brownian motion with the same Hurst parameter of the continuous‐time process from which the aggregates are measured. These results are then used to assess the loss of forecasting efficiency due to aggregation.

Suggested Citation

  • Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary and Non‐stationary Continuous‐Time Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 583-597, December.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:4:p:583-597
    DOI: 10.1111/j.1467-9469.2005.00455.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2005.00455.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2005.00455.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Henghsiu Tsai & K. S. Chan, 2005. "Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 691-713, September.
    2. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, September.
    3. Beran, Jan & Ocker, Dirk, 2000. "Temporal aggregation of stationary and nonstationary FARIMA (p, d, 0) models," CoFE Discussion Papers 00/22, University of Konstanz, Center of Finance and Econometrics (CoFE).
    4. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Man Kasing, 2010. "Extended Fractional Gaussian Noise and Simple ARFIMA Approximations," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-26, September.
    2. repec:hal:journl:peer-00815563 is not listed on IDEAS
    3. Theodore Simos & Mike Tsionas, 2018. "Bayesian inference of the fractional Ornstein–Uhlenbeck process under a flow sampling scheme," Computational Statistics, Springer, vol. 33(4), pages 1687-1713, December.
    4. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
    5. Michael A. Thornton & Marcus J. Chambers, 2013. "Continuous-time autoregressive moving average processes in discrete time: representation and embeddability," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 552-561, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beran, Jan & Schützner, Martin & Ghosh, Sucharita, 2010. "From short to long memory: Aggregation and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2432-2442, November.
    2. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    3. Prilly Oktoviany & Robert Knobloch & Ralf Korn, 2021. "A machine learning-based price state prediction model for agricultural commodities using external factors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1063-1085, December.
    4. David Bolder & Shudan Liu, 2007. "Examining Simple Joint Macroeconomic and Term-Structure Models: A Practitioner's Perspective," Staff Working Papers 07-49, Bank of Canada.
    5. Yuo-Hsien Shiau & Su-Fen Yang & Rishan Adha & Syamsiyatul Muzayyanah, 2022. "Modeling Industrial Energy Demand in Relation to Subsector Manufacturing Output and Climate Change: Artificial Neural Network Insights," Sustainability, MDPI, vol. 14(5), pages 1-18, March.
    6. Clements, Kenneth W. & Fry, Renée, 2008. "Commodity currencies and currency commodities," Resources Policy, Elsevier, vol. 33(2), pages 55-73, June.
    7. Faust, Jon & Gupta, Abhishek, 2010. "Posterior Predictive Analysis for Evaluating DSGE Models," MPRA Paper 26721, University Library of Munich, Germany.
    8. Rutger-Jan Lange & Coen N. Teulings, 2021. "The option value of vacant land: Don't build when demand for housing is booming," Tinbergen Institute Discussion Papers 21-022/IV, Tinbergen Institute.
    9. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    10. Zirogiannis, Nikolaos & Tripodis, Yorghos, 2013. "A Generalized Dynamic Factor Model for Panel Data: Estimation with a Two-Cycle Conditional Expectation-Maximization Algorithm," Working Paper Series 142752, University of Massachusetts, Amherst, Department of Resource Economics.
    11. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    12. Moshe Buchinsky & Phillip Leslie, 2010. "Educational Attainment and the Changing U.S. Wage Structure: Dynamic Implications on Young Individuals' Choices," Journal of Labor Economics, University of Chicago Press, vol. 28(3), pages 541-594, July.
    13. S. Boragan Aruoba & Francis X. Diebold, 2010. "Real-Time Macroeconomic Monitoring: Real Activity, Inflation, and Interactions," American Economic Review, American Economic Association, vol. 100(2), pages 20-24, May.
    14. Ippei Fujiwara & Koji Takahashi, 2012. "Asian Financial Linkage: Macro‐Finance Dissonance," Pacific Economic Review, Wiley Blackwell, vol. 17(1), pages 136-159, February.
    15. Hongsheng Bi & Rubao Ji & Hui Liu & Young-Heon Jo & Jonathan A Hare, 2014. "Decadal Changes in Zooplankton of the Northeast U.S. Continental Shelf," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-12, January.
    16. Reema Gh. Alajmi, 2024. "Energy Consumption and Carbon Emissions: An Empirical Study of Saudi Arabia," Sustainability, MDPI, vol. 16(13), pages 1-16, June.
    17. Leif Anders Thorsrud, 2016. "Nowcasting using news topics. Big Data versus big bank," Working Paper 2016/20, Norges Bank.
    18. Knut Are Aastveit & Karsten R. Gerdrup & Anne Sofie Jore & Leif Anders Thorsrud, 2014. "Nowcasting GDP in Real Time: A Density Combination Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 48-68, January.
    19. Obryan Poyser, 2017. "Exploring the determinants of Bitcoin's price: an application of Bayesian Structural Time Series," Papers 1706.01437, arXiv.org.
    20. Škare, Marinko & Mošnja-Škare, Lorena, 2019. "Economic policy implications of the Gibson Law in the Netherlands (1800–2012)," Journal of Policy Modeling, Elsevier, vol. 41(5), pages 926-942.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:32:y:2005:i:4:p:583-597. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.