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Cross-Sectional Aggregation and Persistence in Conditional Variance

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  • Menelaos Karanasos
  • Zacharias Psaradakis
  • Martin Sola

Abstract

This paper explores the interactions between cross-sectional aggregation and persistence of volatility shocks. We derive the ARMA-GARCH representation that linear aggregates of ARMA processes with GARCH errors admit, and establish conditions under which persistence in volatility of the aggregate series is higher than persistence in the volatility of the individual series. The practical implications of the results are illustrated empirically in the context of an option pricing exercise.

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  • Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, "undated". "Cross-Sectional Aggregation and Persistence in Conditional Variance," Discussion Papers 00/09, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:00/09
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2000/0009.pdf
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    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    3. 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.
    4. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    5. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    6. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    7. Poterba, James M & Summers, Lawrence H, 1986. "The Persistence of Volatility and Stock Market Fluctuations," American Economic Review, American Economic Association, vol. 76(5), pages 1142-1151, December.
    8. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    9. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
    12. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    13. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Menelaos Karanasos, "undated". "The Covariance Structure of Component and Multivariate Garch Models," Discussion Papers 99/12, Department of Economics, University of York.
    2. Menelaos Karanasos, "undated". "Some Exact Formulae for the Constant Correlation and Diagonal M - Garch Models," Discussion Papers 00/14, Department of Economics, University of York.
    3. Menelaos Karanasos, "undated". "The Covariance Structure of Mixed ARMA Models," Discussion Papers 00/10, Department of Economics, University of York.
    4. Li, Chang-Shuai, 2012. "Common persistence in conditional variance: A reconsideration," Economic Modelling, Elsevier, vol. 29(5), pages 1809-1819.

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    Keywords

    ARMA process; Cross-sectional aggregation; GARCH process; Volatility persistence.;
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