Outliers and misleading leverage effect in asymmetric GARCH-type models

This paper illustrates how outliers can affect both the estimation and testing of leverage effect by focusing on the TGARCH model. Three estimation methods are compared through Monte Carlo experiments: Gaussian Quasi-Maximum Likelihood, Quasi-Maximum Likelihood based on the Student-t likelihood and Least Absolute Deviation method. The empirical behavior of the t-ratio and the Likelihood Ratio tests for the significance of the leverage parameter is also analyzed. Our results put forward the unreliability of Gaussian Quasi-Maximum Likelihood methods in the presence of outliers. In particular, we show that one isolated outlier could hide true leverage effect whereas two consecutive outliers bias the estimated leverage coefficient in a direction that crucially depends on the sign of the first outlier and could lead to wrongly reject the null of no leverage effect or to estimate asymmetries of the wrong sign. By contrast, we highlight the good performance of the robust estimators in the presence of one isolated outlier. However, when there are patches of outliers, our findings suggest that the sizes and powers of the tests as well as the estimated parameters based on robust methods may still be distorted in some cases. We illustrate these results with two series of daily returns.