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Inference in ARCH and GARCH models with heavy-tailed errors


  • Hall, Peter
  • Yao, Qiwei


ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy–tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy–tailed errors, the asymptotic distributions of quasi–maximum likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile–t, subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically.

Suggested Citation

  • Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:5875

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    More about this item


    autoregression; bootstrap; dependent data; domain of attraction; financial data; limit theory; percentile–t bootstrap; quasi–maximum likelihood; semiparametric inference; stable law; studentize; subsample bootstrap; time series;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General


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