A robust closed-form estimator for the GARCH(1,1) model

Abstract

In this paper we extend the closed-form estimator for the generalized autoregressive conditional heteroscedastic (GARCH(1,1)) proposed by Kristensen and Linton [A closed-form estimator for the GARCH(1,1) model. Econom Theory. 2006;22:323–337] to deal with additive outliers. It has the advantage that is per se more robust that the maximum likelihood estimator (ML) often used to estimate this model, it is easy to implement and does not require the use of any numerical optimization procedure. The robustification of the closed-form estimator is done by replacing the sample autocorrelations by a robust estimator of these correlations and by estimating the volatility using robust filters. The performance of our proposal in estimating the parameters and the volatility of the GARCH(1,1) model is compared with the proposals existing in the literature via intensive Monte Carlo experiments and the results of these experiments show that our proposal outperforms the ML and quasi-maximum likelihood estimators-based procedures. Finally, we fit the robust closed-form estimator and the benchmarks to one series of financial returns and analyse their performances in estimating and forecasting the volatility and the value-at-risk.