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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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    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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