GEL Estimation for Semi-Strong Non-Linear GARCH with Robust Empirical Likelihood Inference

The presentation is based on the construction of Generalized Empirical Likelihood estimators for Nonlinear GARCH models with possibly heavy tailed non-iid errors. The estimators imbed tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality and efficiency for very heavy-tailed data due to feedback or idiosyncratic noise. The authors show the empirical probabilities from Euclidean Empirical Likelihood optimize weight for usable large values, give large but not maximum weight on extremes, and give the lowest weight to non-leverage points. Finally, the authors use tail-trimmed GEL empirical probabilities for efficient and robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and moment estimation with an application to heavy tail robust and efficient Expected Shortfall estimation.