Robust Inference Theory for Non-Regular Time Series Models and Its Extensions

Abstract

We construct robust inference theories for time series models under non-regular settings such as innite variance and long-range dependence. In such non-regular models, the rates of convergence and limit distributions of typical statistics depend on unknown nuisance parameters, making it challenging to establish statistical inference methods based on these distributions. To address these problems, we employ robust methodologies such as self-normalization, self-weighting, and empirical likelihood approach. Under mild conditions of dependence structure and higher-order moments of the models, we construct robust statistics which have desired limit distributions. In addition, we apply the proposed method to change point analysis and tests of causality.