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Contemporaneous Aggregation of GARCH Models and Evaluation of the Aggregation Bias

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  • Eric Jondeau

    (University of Lausanne and Swiss Finance Institute)

Abstract

It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics of the aggregate volatility involves additional lags that reflect the moments of the distribution of the individual persistence parameters. Then the paper describes a consistent estimator of the aggregate process, based on nonlinear least squares. A simulation study reveals that this aggregation-corrected estimator performs very well under realistic sets of parameters. Last, this approach is extended to a multi-sector context. This extension is used to evaluate the importance of the aggregation bias. Using size and book-to-market portfolios, I show that the investor is willing to pay one fifth of her expected return to switch from the standard GARCH (1,1) estimator to the aggregation-corrected estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:chf:rpseri:rp0806
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    File URL: http://ssrn.com/abstract=1105784
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    References listed on IDEAS

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    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
    3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    4. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    5. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    6. Francq, Christian & Zakoïan, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, vol. 16(5), pages 692-728, October.
    7. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
    8. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    9. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    10. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    11. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    12. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
    13. Mark Carey & René M. Stulz, 2007. "The Risks of Financial Institutions," NBER Books, National Bureau of Economic Research, Inc, number care06-1, March.
    14. Hafner, Christian M., 2008. "Temporal aggregation of multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 142(1), pages 467-483, January.
    15. Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    16. Lewbel, Arthur, 1994. "Aggregation and Simple Dynamics," American Economic Review, American Economic Association, vol. 84(4), pages 905-918, September.
    17. Fama, Eugene F & French, Kenneth R, 1995. "Size and Book-to-Market Factors in Earnings and Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 131-155, March.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 433-495.
    20. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    21. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    22. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    23. Komunjer, Ivana, 2001. "Consistent Estimation for Aggregated GARCH," University of California at San Diego, Economics Working Paper Series qt1fp2v3q7, Department of Economics, UC San Diego.
    24. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
    25. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Contemporaneous aggregation; Heterogeneity; Volatility; GARCH model.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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