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Least absolute deviations estimation for ARCH and GARCH models

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  • Peng, Liang
  • Yao, Qiwei

Abstract

Hall & Yao (2003) showed that, for ARCH/GARCH, i.e. autoregressive conditional heteroscedastic/generalised autoregressive conditional heteroscedastic, models with heavy‐tailed errors, the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow convergence rates. In this paper three types of absolute deviations estimator have been examined, and the one based on logarithmic transformation turns out to be particularly appealing. We have shown that this estimator is asymptotically normal and unbiased. Furthermore it enjoys the standard convergence rate of n1/2 regardless of whether the errors are heavy‐tailed or not. Simulation lends further support to our theoretical results.

Suggested Citation

  • Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:5828
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    File URL: http://eprints.lse.ac.uk/5828/
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    Keywords

    ARCH; asymptotic normality; GARCH; gaussian likelihood; heavy tail; least absolute deviations estimator; maximum quasilikelihood estimator; Time series.;
    All these keywords.

    JEL classification:

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

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