Departmental Colloquia: Fumiya Akashi



Department of Applied Mathematics, School of Fundamental Science & Engineering
Waseda University


Robust Statistical Inference for Non-Standard Time Series Models by Empirical Likelihood, Self-Weighting and Self-Normalization



In these few decades, non-standard aspects of real data are frequently observed in practical situations. For example, Mandelbrot (1963, J. Polit. Econ.) and Fama (1965, J. Bus.) found heavy-tailed economic data which were poorly captured by the Gaussian models. On the other hand, a prominent example of long-range dependence was found by Hurst (1951, Trans. Amer. Soc. Civil Eng.) via the analysis of records of water flows through the Nile and other rivers. To model such data suitably, we frequently consider heavy-tailed and/or long-memory processes. However, it is well known that the limit distributions of fundamental statistics (e.g., sample mean) are not expressed in a closed form under the presence of heavy-tails and long-range dependence. Because of the involved limit distributions, it is unfeasible to obtain cut-off points of a confidence interval or critical values of tests in practice. So in this talk, we consider the empirical likelihood method and provide new statistical inference procedures. The empirical likelihood method proposed by Owen (1988, Biometrika) enables us to construct nonparametric likelihood ratio without knowledge of the underlying distribution. Especially, we modify the empirical likelihood statistic by self-weighting methods, and show that the proposed statistics have standard chi-square limit distribution. Moreover, we overcome the difficulties brought by heavy-tails and long-range dependence of the models by the self-normalized subsampling method proposed by Bai et al. (2016, Ann. Stat.). Finally, a unified and robust framework for various time series models under the non-standard situation is established.






Friday, 2/23/2018, BLOC 113, 11:30 AM