Bounded Influence Estimation and Outlier Detection for GARCH Models With an Application to Foreign Exchange Rates

In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for GARCH models. Previous studies show that maximum likelihood estimates of GARCH models are sensitive to outliers and financial time series present a heavy tail due to outliers. The proposed BIE limits the influence of a small subset of the data and is asymptotically normal. Its robustness against outliers and model misspecification is examined and supported. We further use BIE with GARCH models to develop a method for detection of additive outliers. An application to the exchange rates of major currencies is provided. * Correspondence author. Address: 413 Hayden Hall, Finance and Insurance Group, Northeastern University, Boston, MA 02115, USA. Telephone: 1-617-373-4707. Fax: 1-617-373-8798. Email: [email protected]. Bounded Influence Estimation and Outlier Detection for GARCH With an Application to Foreign Exchange Rates