Identifying infinite variance ARMA models using a robust Pukkila Koreisha Kallinen strategy

We introduce and evaluate a new approach to parameter estimation and model selection for infinite variance ARMA processes. This is based on a robust analogue of the Pukkila-Koreisha-Kallinen strategy which gives substantial improvements in performance for heavy tailed innovations. A significant feature of our experiments is the inclusion of model selection effects on parameter estimation. We also comment on the value of certain model selection criteria for Whittle's approach which may be of independent interest.