Using GARCH Volatility Filtering Before Extreme-Value Risk Analysis

Summary

The document raises a modeling question about combining GARCH volatility filtering with peaks-over-threshold extreme value theory (POT) and Markov chain Monte Carlo estimation. The researcher fits several conditional volatility specifications, including standard and asymmetric variants, then observes that standardized returns appear less heavy-tailed than the original return series. They wonder whether an over-responsive volatility model is removing variation that the tail model needs, and whether a simpler EWMA filter might work better.

The text provides no answers, empirical comparisons, or diagnostic results beyond that observation. It therefore frames a useful risk-modeling issue rather than establishing that GARCH is unsuitable or that EWMA is preferable. Any conclusion would depend on the innovation distribution, model fit, residual diagnostics, threshold selection, and the purpose of filtering. Researchers can use the question to motivate checking whether standardized residuals are adequately specified before fitting POT, and to compare filters on consistent out-of-sample risk measures.

Key ideas

• GARCH filtering can alter the apparent tail thickness of return residuals.
• POT modeling is sensitive to the distribution of the filtered series used for threshold exceedances.
• Compare volatility filters such as GARCH and EWMA using residual diagnostics and consistent risk criteria.
• The document poses the concern but supplies no evidence that one filter is superior.

Tags

# GARCH filtering and extreme value theory


# GARCH filtering and extreme value theory












We are evaluating a model for risk management based on extreme value theory using peaks over threshold and markov chain monte carlo methods.

In doing this, we are firstly fitting a GARCH (we have tried GARCH(1,1), E-GARCH, Asymmetric GARCH, GJR-GARCH, ...) model in order to filter the return series.

We are encountering a problem here however, wherein our filtered return distribution is far less leptokurtic than the original one, even when we use e.g. Student T or Generalized Hyperbolic distributions for the innovations. Informally speaking, we feel the GARCH model is over-reactive and negatively affects the subsequent POT step.

Are we missing something here? Is it, in practice, better to use a simpler (e.g. EWMA) volatility model? Any insight is highly appreciated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.