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A0246
Title: Robust GEL method for linear hypothesis of infinite variance processes Authors:  Fumiya Akashi - University of Tokyo (Japan) [presenting]
Abstract: Testing general linear hypotheses on the coefficient of ARMA models with possibly infinite variance error terms is considered. If the model may have infinite variance, it is well known that the rate of convergence of fundamental statistics (e.g., sample mean) depends on the unknown tail-index of innovation processes, and the limit distribution is not represented in a closed form in general. As a result, it is often difficult in practice to decide cut-off points of confidence intervals or critical values of tests when we apply classical methods such as the maximum likelihood ratio test directly. To overcome the difficulties, the self-weighted generalized empirical likelihood (GEL) method is constructed, and the proposed GEL statistic converges to the chi-square distribution regardless whether the model has infinite variance or not. That is, the proposed test statistic is shown to be robust against the heavy-tails of the model. Therefore, various important tests involving model diagnostics can be carried out with no prior estimation for the unknown quantity of the models such as the tail-index of the innovations. Some simulation experiments also illustrate that the proposed test performs better than the classical self-weighted Wald-type test.