The issue of detecting and handling outliers in GARCH processes has received considerable attention recently. In this chapter, we put forwardan iterative outlier detection procedure, which is appropriate given that in practice both the number of outliers as well as their timing is unknown. Our procedure aims to test for the presence of a single outlier at a time. Upon detection of an outlier in the original time series, the relevant observation is adjusted accordingly, and the modified series is tested again for the presence of a(nother) single outlier. This process continues until no further outliers are detected. The asymptotic distribution of the outlier detection test statistic is found to be nonstandard and not pivotal. Critical values for a number of representative parameterizations and sample sizes are provided. A bootstrap procedure is also discussed. We evaluate our method in an extensive simulation study. The results indicate that the procedure works remarkably well, also in the presence of multiple outliers.We outline extensions of the outlier detection method for higher-order GARCH processes and for processes with linear (ARMA) dynamics for the conditional mean. An application to daily stock index return series shows that correcting for a few outliers yields considerable improvements in out-of-sample forecasts of conditional volatility.

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Keywords generalized autoregressive conditional heteroskedasticity (GARCH) model
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Franses, Ph.H.B.F, & van Dijk, D.J.C. (2010). GARCH, outliers, and forecasting volatility. In Nonlinear Financial Econometrics: Forecasting Models, Computational and Bayesian Models (pp. 136–159). doi:10.1057/9780230295223_8