The analysis of marked and weighted empirical processes of estimated residuals

Working paper

An extended and improved theory is presented for marked and weighted empirical processes of residuals of time series regressions. The theory is motivated by 1-step Huber-skip estimators, where a set of good observations are selected using an initial estimator and an updated estimator is found by applying least squares to the selected observations. In this case, the weights and marks represent powers of the regressors and the regression errors, respectively. The inclusion of marks is a non-trivial extention to previous theory and requires refined martingale arguments.

Authors: Berenguer Rico, V; Nielsen, B; Johansen, S

• Publication status: Published
• Publisher: University of Oxford
• Series: Department of Economics Discussion Paper Series
• Publication date: 2019-05-06
• Paper number: 870
• Keywords: 1-step Huber-skip; robust statistics; stationarity; non-stationarity