Estimation and Inference in Arch Models in the Presence of Outliers

In this paper, we show the effects that outliers have on estimation and inference for autoregressive conditional heteroskedasticity (ARCH) models. We propose for a wide class of ARCH models commonly estimated, an empirically tractable solution to this problem by replacing outliers with their conditional expectations (optimal forecasts) in the likelihood function. This solution works well in both simulations and applications, as opposed to dummy variables which can lead to multimodality in the ARCH likelihood and invalid inference. We demonstrate the accuracy of our procedure for parameter estimation and forecasting. The empirical examples include U.S. interest rate, foreign exchange rate, and stock index data. In addition, we suggest a robust bootstrap test for outliers and evaluate this against the Andrews (2003) S test