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

  • Eric Hillebrand

    (Stanford University)

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.

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File URL: http://128.118.178.162/eps/em/papers/0301/0301003.pdf
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Paper provided by EconWPA in its series Econometrics with number 0301003.

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Length: 27 pages
Date of creation: 24 Jan 2003
Date of revision:
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.
Contact details of provider: Web page: http://128.118.178.162

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  1. 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.
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  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 225-34, April.
  18. 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.
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