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Activity Number:
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19
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Type:
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Contributed
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Date/Time:
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Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Business & Economics Statistics Section
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| Abstract - #301765 |
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Title:
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Volatility Forecasting with GARCH Models when the Fourth Moment Does Not Exist
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Author(s):
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Yasemin Bardakci*+ and Matthew L. Higgins
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Companies:
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Western Michigan University and Western Michigan University
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Address:
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Dept. of Economics, Kalamazoo, MI, 49008,
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Keywords:
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GARCH ; volatility forecasting ; Monte Carlo
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Abstract:
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Although GARCH models fit extremely well in sample, many authors have claimed that GARCH models fail to predict volatility out of sample. The R^2 between the realized volatility and predicted volatility are typically less than .1, suggesting that ARCH models are misspecified. Recently, Andersen and Bollerslev (1988) countered this argument. Assuming the fourth moment of returns exists, they showed that a small observed R^2 is consistent with the mathematically expected R^2. We examine whether the results of Andersen and Bollerslev extend to the case when the expected R^2 does not exist. GARCH models should forecast return volatility well when volatility is highly persistent and the fourth moment of returns does not exist. We study the sampling distribution of the R^2 with a Monte Carlo simulation. Using generated samples from different integrated in variance GARCH models, we estimate the CDF of the R^2 between realized and predicted volatility. We tabulate percentiles of the sampling distribution to provide a guide to determine whether an observed R^2 from volatility prediction is consistent with an estimated model.
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