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Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models

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  • Eric Hillebrand

    (Stanford University)

Abstract

A common finding in the empirical literature is that financial volatility exhibits high persistence, or slow mean reversion of the order of months. We present evidence that financial volatility data contains more than a single time scale. After showing that the expectation of the sum of the estimates of the autoregressive coefficients of a GARCH(1,1) model is one when there are unknown parameter changes, we explore the phenomenon in simulations. For parameter changes within realistic ranges for stock-price volatility we obtain global estimates close to integration while the average data- generating mean reversion is of the order of a few days. Spectral analysis of the Dow Jones Industrial Average and the S&P500 index between 1985 and 2001 reveals a short time scale of the magnitude of 5- 10 days present in the data. Thus, two different time scales exist in the data, one of the order of months corresponding to different volatility regimes, and one of the order of days corresponding to the average mean reversion within regimes.

Suggested Citation

  • Eric Hillebrand, 2003. "Overlaying Time Scales and Persistence Estimation in GARCH(1,1) Models," Econometrics 0301003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0301003
    Note: Type of Document - Tex; prepared on IBM PC; to print on HP/PostScript; pages: 27 ; figures: included. pdf-file.
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. 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.
    3. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    4. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    6. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    7. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    8. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    9. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    12. Thomas Mikosch & Catalin Starica, 2004. "Long range dependence effects and ARCH modelling," Econometrics 0412004, University Library of Munich, Germany.
    13. B. B. Mandelbrot, 2001. "Stochastic volatility, power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 558-559.
    14. Blake LeBaron, 2001. "Volatility," Computing in Economics and Finance 2001 108, Society for Computational Economics.
    15. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    16. 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.
    17. 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.
    18. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    19. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    20. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    21. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    22. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
    23. 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. Matthew Lorig, 2010. "Time-Changed Fast Mean-Reverting Stochastic Volatility Models," Papers 1010.5203, arXiv.org, revised Apr 2012.
    2. Jean-Pierre Fouque & Matthew Lorig, 2010. "A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model," Papers 1007.4366, arXiv.org, revised Apr 2012.

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    More about this item

    Keywords

    GARCH; volatility persistence; regime switching; long memory; short memory; structural change;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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