Least absolute deviations estimation for ARCH and GARCH models

Liang Peng

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Financial Risk and Volatility Modeling Advanced Statistical Methods and Models Statistical and numerical algorithms

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.

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2006Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models 2007Robust estimates for GARCH models 2013Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods 2011Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models 2006Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations 2011Estimating GARCH volatility in the presence of outliers 2006Recent Advances in ARCH Modelling 2007Estimation and tests for power-transformed and threshold GARCH models

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