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Outlier detection algorithms for least squares time series regression

Author

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  • Søren Johansen

    (University of Copenhagen and CREATES)

  • Bent Nielsen

    (Nuffield College & Department of Economics, University of Oxford & Institute for New Economic Thinking at the Oxford Martin School.)

Abstract

We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator Saturation, iterated 1-step Huber-skip M-estimators and the Forward Search. These methods classify observations as outliers or not. From the asymptotic results we establish a new asymptotic theory for the gauge of these methods, which is the expected frequency of falsely detected outliers. The asymptotic theory involves normal distribution results and Poisson distribution results. The theory is applied to a time series data set.

Suggested Citation

  • Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," CREATES Research Papers 2014-39, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-39
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    References listed on IDEAS

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    Citations

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    Cited by:

    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. David H. Bernstein & Bent Nielsen, 2019. "Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient," Econometrics, MDPI, vol. 7(1), pages 1-24, January.
    3. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, vol. 3(1), pages 1-31, March.

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    More about this item

    Keywords

    Huber-skip M-estimators; 1-step Huber-skip M-estimators; iteration; Forward Search; Impulse Indicator Saturation; Robusti?ed Least Squares; weighted and marked empirical processes; iterated martingale inequality; gauge;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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