The Analysis of Marked and Weighted Empirical Processes of Estimated Residuals

30 Pages Posted: 28 May 2019

See all articles by Vanessa Berenguer-Rico

Vanessa Berenguer-Rico

University of Barcelona - Department of Econometrics

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Bent Nielsen

University of Oxford - Department of Economics

Date Written: April 2019

Abstract

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.

Keywords: 1-Step Huber-Skip; Non-Stationarity; Robust Statistics; Stationarity

JEL Classification: C130

Suggested Citation

Berenguer-Rico, Vanessa and Johansen, Soren and Nielsen, Bent, The Analysis of Marked and Weighted Empirical Processes of Estimated Residuals (April 2019). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 19-05, Available at SSRN: https://ssrn.com/abstract=3380967 or http://dx.doi.org/10.2139/ssrn.3380967

Vanessa Berenguer-Rico (Contact Author)

University of Barcelona - Department of Econometrics ( email )

Av. Diagonal 690
Barcelona, E-08034
Spain

Soren Johansen

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Bent Nielsen

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom

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