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Outlier detection algorithms for least squares time series regression

Author

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  • Søren Johansen

    (Dept of Economics, University of Copenhagen and CREATES, Dept of Economics and Business, Aarhus University)

  • Bent Nielsen

    (Nuffield College and Dept of Economics)

Abstract

We review recent asymptotic results on some robust methods for multiple regres- sion. 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 as- ymptotic 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," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1404
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    References listed on IDEAS

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    Cited by:

    1. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, vol. 3(1), pages 1-31, March.
    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. 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.

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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 em- pirical 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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