A New Class of Robust Observation-Driven Models

Abstract

This paper introduces a new class of observation-driven models, including score models as a special case. This new class inherits and extends the basic ideas behind the development of score models and addresses a number of unsolved issues in the score literature. In particular, the new class of models (i) allows QML estimation of static parameters, (ii) allows the production of leverage effects in the presence of negative outliers, (iii) allows update asymmetry and asymmetric forecast loss functions in the presence of symmetric or skewed innovations, and (iii) achieves out-of-sample outlier robustness in the presence of sub-exponential tails. We establish the asymptotic properties of the QLE, QMLE, and MLE as well as likelihood ratio and Lagrange multiplier test statistics. The finite sample properties are studied by means of an extensive Monte Carlo study. Finally, we show the empirical relevance of this new class of models on real data.