Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models

This paper develops the generalized empirical likelihood (GEL) method for infinite variance ARMA models, and constructs a robust testing procedure for general linear hypotheses. In particular, we use the GEL method based on the least absolute deviations and self-weighting, and construct a natural class of statistics including the empirical likelihood and the continuous updating-generalized method of moments for infinite variance ARMA models. The self-weighted GEL test statistic is shown to converge to a \(\chi ^2\)-distribution, although the model may have infinite variance. Therefore, we can make inference without estimating any unknown quantity of the model such as the tail index or the density function of unobserved innovation processes. We also compare the finite sample performance of the proposed test with the Wald-type test by Pan et al. (Econom Theory 23:852–879, 2007) via some simulation experiments.