Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors

We present a robust Generalized Empirical Likelihood estimator and confidence region for the parameters of an autoregression that may have a heavy tailed heteroscedastic error. The estimator exploits two transformations for heavy tail robustness: a redescending transformation of the error that robustifies against innovation outliers, and weighted least squares instruments that ensure robustness against heavy tailed regressors. Our estimator is consistent for the true parameter and asymptotically normally distributed irrespective of heavy tails.