Title: Robust statistical inference for time series regression model by self-normalized subsampling method
Authors: Fumiya Akashi - The University of Tokyo (Japan) [presenting]
Shuyang Bai - University of Georgia (United States)
Murad Taqqu - Boston University (United States)
Abstract: Robust statistical inference for possibly long-memory and/or heavy-tailed processes is considered. In the context of time series analysis, we often observe heavy-tailed and long-range dependent data in variety of fields. To model such data suitably, we consider a linear regression model with dependent covariate and error processes. When the model has heavy-tails or long-memory, it is well known that fundamental statistics (e.g., sample mean) converge to involved distributions and the rate of convergence of the statistic contains unknown tail-index and Hurst index. To overcome such difficulties, we propose the self-normalized statistic and subsampling procedures. As a result, we construct a confidence region for the regression parameter of the model without any prior estimation of nuisance parameters. Some simulation experiments illustrate the finite sample performance of the proposed method.