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Tightness of M-estimators for multiple linear regression in time series

Author

Listed:
  • 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 show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary an random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

Suggested Citation

  • Søren Johansen & Bent Nielsen, 2016. "Tightness of M-estimators for multiple linear regression in time series," CREATES Research Papers 2016-18, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2016-18
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/16/rp16_18.pdf
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    References listed on IDEAS

    as
    1. Chen, X. R. & Wu, Y. H., 1988. "Strong consistency of M-estimates in linear models," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 116-130, October.
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    More about this item

    Keywords

    M-estimator; robust statistics; martingales; Huber-skip; quantile estimation.;
    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

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