Title: Self-weighted GEL method for heavy-tailed ARMA models and its applications to various problems
Authors: Fumiya Akashi - The University of Tokyo (Japan) [presenting]
Abstract: A testing problem of linear hypothesis on the coefficients of heavy-tailed ARMA processes is considered. It is well known that heavy-tail phenomena of time series models are known to cause some problem, such as intractable form of the rate of convergence or complicated limit distribution. As a result, it is often difficult to detect critical values of tests or cut-off points of confidence interval based on the limit distribution of test statistics in infinite variance cases. To overcome the difficulties, the aim is to construct the least absolute deviations regression and self-weighting-based generalized empirical likelihood (GEL) statistics for the testing problem of ARMA models. By the self-weighting and GEL, the proposed test statistic is shown to have a pivotal chi-squared limit distribution regardless of whether the model has infinite variance or not. In the latter half of this talk, we apply the self-weighted GEL method to the test of causality and change-point detection problem of heavy-tailed time series models.