Self-weighted GEL Methods for Infinite Variance Processes
This chapter focuses on an alternative robust estimation/testing procedure for possibly infinite variance time series models. In the context of inference for heavy-tailed observation, least absolute deviations (LAD) estimators are known to be less sensitive to outliers than the classical least squares regression. This section generalizes the LAD regression-based inference procedure to the self-weighted version, which is a concept originally introduced by Ling (2005) for AR processes. Using the self-weighting method, we extend the generalized empirical likelihood (GEL) method to possibly infinite variance process, and construct feasible and robust estimation/testing procedures. The former half of this chapter provides a brief introduction to the LAD regression method for possibly infinite variance ARMA models, and construct the self-weighted GEL statistic following Akashi (2017). The desirable asymptotic properties of the proposed statistics will be elucidated. The latter half of this chapter illustrates an important application of the self-weighted GEL method to the change point problem of time series models.