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The analysis of marked and weighted empirical processes of estimated residuals

Author

Listed:
  • Vanessa Berenguer-Rico

    () (Department of Economics and Mansfield College, University of Oxford)

  • Søren Johansen

    () (University of Copenhagen and CREATES and Aarhus University)

  • Bent Nielsen

    () (Department of Economics and Nuffield College, University of Oxford)

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.

Suggested Citation

  • Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1903
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    File URL: https://www.nuffield.ox.ac.uk/economics/Papers/2019/2019W03_VSB_EP_DP.pdf
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    References listed on IDEAS

    as
    1. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    2. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, July.
    3. Søren Johansen & Bent Nielsen, 2016. "Rejoinder: Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 374-381, June.
    4. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Vanessa Berenguer Rico & Bent Nielsen & Søren Johansen, 2019. "Uniform Consistency of Marked and Weighted Empirical Distributions of Residuals," Economics Series Working Papers 871, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    1-step Huber-skip; Non-stationarity; Robust Statistics; Stationarity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    Statistics

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