Bounded influence estimator for GARCH models: evidence from foreign exchange rates

Abstract

Previous research indicates that the maximum likelihood estimates of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models on foreign exchange rates, under various distributional assumptions, are sensitive to the presence of outliers. The advantage of the proposed Bounded Influence Estimator (BIE) is that it limits the influence of a small subset of data and is asymptotically normal. The BIE provides more consistent and robust estimates than Maximum Likelihood Estimator (MLE) and semi-parametric estimator, both of which tend to underestimate volatility persistence due to outliers. It is thus robust to outliers and model misspecification. Results of BIE estimates of GARCH models on the exchange rate series of five major currencies indicate that BIE offers an efficient mechanism for down-weighting outlying observations and is a competitive alternative to MLE.

Notes

¹ The Federal Reserve Bank of Chicago provided the daily foreign exchange rate data.

² The empirical results on the ARCH(1) processes are not reported.