IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v28y2007i4p521-544.html
   My bibliography  Save this article

Contemporaneous aggregation of GARCH processes

Author

Listed:
  • Paolo Zaffaroni

Abstract

. In this article, the effect of contemporaneous aggregation of heterogeneous generalized autoregressive conditionally heteroskedastic (GARCH) processes, as the cross‐sectional size diverges to infinity is studied. We analyse both cases of cross‐sectionally dependent and independent individual processes. The limit aggregate does not belong to the class of GARCH processes. Dynamic conditional heteroskedasticity is only preserved when the individual processes are sufficiently cross‐correlated, although long memory for the limit aggregate volatility is not attainable. We also explore more general forms of cross‐sectional dependence and various types of aggregation schemes.

Suggested Citation

  • Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:4:p:521-544
    DOI: 10.1111/j.1467-9892.2006.00522.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2006.00522.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-9892.2006.00522.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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, 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. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
    2. Jan Beran & Haiyan Liu & Sucharita Ghosh, 2020. "On aggregation of strongly dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 690-710, September.
    3. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    4. Gómez-Déniz, E., 2004. "A note on mixture prior distributions with applications in actuarial statistic/Sobre las Distribuciones a Priori Mixtas con Aplicaciones en la Estadística Actuarial," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 372(15á)-37, Agosto.
    5. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    6. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    7. Feng, Yuanhua & Zhou, Chen, 2015. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," International Journal of Forecasting, Elsevier, vol. 31(2), pages 349-363.
    8. Dmitrij Celov & Remigijus Leipus & Anne Philippe, 2010. "Asymptotic normality of the mixture density estimator in a disaggregation scheme," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 425-442.
    9. Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 165-172, August.
    10. Pellegrini, Santiago & Ruiz, Esther & Espasa, Antoni, 2010. "Conditionally heteroscedastic unobserved component models and their reduced form," Economics Letters, Elsevier, vol. 107(2), pages 88-90, May.
    11. 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.
    12. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    13. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2010. "Contemporaneous aggregation and long-memory property of returns and volatility in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4844-4854.
    14. Eric Jondeau, 2008. "Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias," Swiss Finance Institute Research Paper Series 08-06, Swiss Finance Institute.
    15. Zaffaroni, Paolo, 2007. "Aggregation and memory of models of changing volatility," Journal of Econometrics, Elsevier, vol. 136(1), pages 237-249, January.
    16. Eduardo Rossi, 2010. "Univariate GARCH models: a survey (in Russian)," Quantile, Quantile, issue 8, pages 1-67, July.

    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. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    2. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    3. Eduardo Rossi, 2010. "Univariate GARCH models: a survey (in Russian)," Quantile, Quantile, issue 8, pages 1-67, July.
    4. Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 165-172, August.
    5. Gómez-Déniz, E., 2004. "A note on mixture prior distributions with applications in actuarial statistic/Sobre las Distribuciones a Priori Mixtas con Aplicaciones en la Estadística Actuarial," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 372(15á)-37, Agosto.
    6. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    7. Jan Beran & Haiyan Liu & Sucharita Ghosh, 2020. "On aggregation of strongly dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 690-710, September.
    8. Feng, Yuanhua & Zhou, Chen, 2015. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," International Journal of Forecasting, Elsevier, vol. 31(2), pages 349-363.
    9. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    10. Eric Jondeau, 2008. "Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias," Swiss Finance Institute Research Paper Series 08-06, Swiss Finance Institute.
    11. Pellegrini, Santiago & Ruiz, Esther & Espasa, Antoni, 2010. "Conditionally heteroscedastic unobserved component models and their reduced form," Economics Letters, Elsevier, vol. 107(2), pages 88-90, May.
    12. Zaffaroni, Paolo, 2007. "Aggregation and memory of models of changing volatility," Journal of Econometrics, Elsevier, vol. 136(1), pages 237-249, January.
    13. Dmitrij Celov & Remigijus Leipus & Anne Philippe, 2010. "Asymptotic normality of the mixture density estimator in a disaggregation scheme," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 425-442.
    14. 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.
    15. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2010. "Contemporaneous aggregation and long-memory property of returns and volatility in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4844-4854.

    More about this item

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:jtsera:v:28:y:2007:i:4:p:521-544. 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=0143-9782 .

    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.