Estimating GARCH volatility in the presence of outliers

Abstract

a b s t r a c t GARCH volatilities depend on the unconditional variance, which is a non-linear function of the parameters. Consequently, they can have larger biases than estimated parameters. Using robust methods to estimate both parameters and volatilities is shown to outperform Maximum Likelihood procedures.

Volatility persistence in crude oil markets

“…15 13 The estimates of dummies variables are not reported to save space, but they are all significant and available from the authors upon request. 14 The out-of-sample comparison is beyond the scope of this study. Future research is encouraged to address this issue.…”

“…Given the importance of measuring the degree to which past volatilities determine and explain the current volatility, a careful investigation of various possible explanations on this fact should 18 Haldrup and Nielsen (2007) show that an additive outlier may substantially bias the differencing parameter estimate in ARFIMA processes. Carnero et al (2007Carnero et al ( , 2012) and Ng and McAleer (2004) who show that the QML estimators can be severally affected by additive outliers, i.e. both the GARCH parameters can be overestimated or underestimated.…”

“…The comparison between the volatility models is evaluated from various in-sample criteria: LogLikehood (LL), Akaike (AIC), Hannan-Quinn (HQ) and stochastic complexity (RCL) (Rissanen, 1987) criteria. 14 Caporin (2003) show that information criteria can clearly distinguish between long and short memory data generating processes. McKenzie (2003, 2008) find that the HQ and RCL criteria exhibit a clear superiority in their ability to accurately select the correct model for ARCH and GARCH processes.…”

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

“…2 We analyze all the methods of estimation using the mean squared error (MSE) as in Kristensen and Linton (2006) and the biases in the estimation of the volatility as in Carnero et al (2012).…”

“…In the time series literature, it is well known the importance of using robust estimators for measuring the time series dependence. The volatility is estimated by using robust filters proposed by Muler and Yohai (2008) and Carnero et al (2012). Furthermore, the small sample properties of our proposal in the estimation of parameters and volatility are analyzed via intensive Monte Carlo experiments and compared to those of the existing alternatives in the literature.…”