Robust Regression on Stationary Time Series: A Self‐Normalized Resampling Approach

Abstract

This article extends the self‐normalized subsampling method of Bai et al. (2016) to the M‐estimation of linear regression models, where the covariate and the noise are stationary time series which may have long‐range dependence or heavy tails. The method yields an asymptotic confidence region for the unknown coefficients of the linear regression. The determination of these regions does not involve unknown parameters such as the intensity of the dependence or the heaviness of the distributional tail of the time series. Additional simulations can be found in a supplement. The computer codes are available from the authors.