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Robust regression with optimisation heuristics

Author

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  • Manfred Gilli
  • Enrico Schumann

Abstract

Linear regression is widely-used in finance. While the standard method to obtain parameter estimates, Least Squares, has very appealing theoretical and numerical properties, obtained estimates are often unstable in the presence of extreme observations which are rather common in financial time series. One approach to deal with such extreme observations is the application of robust or resistant estimators, like Least Quantile of Squares estimators. Unfortunately, for many such alternative approaches, the estimation is much more difficult than in the Least Squares case, as the objective function is not convex and often has many local optima. We apply different heuristic methods like Differential Evolution, Particle Swarm and Threshold Accepting to obtain parameter estimates. Particular emphasis is put on the convergence properties of these techniques for fixed computational resources, and the techniques’ sensitivity for different parameter settings.

Suggested Citation

  • Manfred Gilli & Enrico Schumann, 2009. "Robust regression with optimisation heuristics," Working Papers 011, COMISEF.
  • Handle: RePEc:com:wpaper:011
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    References listed on IDEAS

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    1. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
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    3. Ozgur S. Ince & R. Burt Porter, 2006. "INDIVIDUAL EQUITY RETURN DATA FROM THOMSON DATASTREAM: HANDLE WITH CARE!," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 29(4), pages 463-479.
    4. Knez, Peter J & Ready, Mark J, 1997. " On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions," Journal of Finance, American Finance Association, vol. 52(4), pages 1355-1382, September.
    5. Manfred Gilli & Evis Këllezi & Hilda Hysi, "undated". "A Data-Driven Optimization Heuristic for Downside Risk Minimization," Swiss Finance Institute Research Paper Series 06-02, Swiss Finance Institute.
    6. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
    7. Peter Winker & Marianna Lyra & Chris Sharpe, 2008. "Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models," Working Papers 006, COMISEF.
    8. Rudolf, Markus & Wolter, Hans-Jurgen & Zimmermann, Heinz, 1999. "A linear model for tracking error minimization," Journal of Banking & Finance, Elsevier, vol. 23(1), pages 85-103, January.
    9. Manfred GILLI & Enrico SCHUMANN, 2009. "An Empirical Analysis of Alternative Portfolio Selection Criteria," Swiss Finance Institute Research Paper Series 09-06, Swiss Finance Institute.
    10. Blume, Marshall E, 1971. "On the Assessment of Risk," Journal of Finance, American Finance Association, vol. 26(1), pages 1-10, March.
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    Cited by:

    1. repec:aoj:ajeaer:2017:p:61-67 is not listed on IDEAS
    2. repec:bla:jorssc:v:66:y:2017:i:5:p:997-1013 is not listed on IDEAS
    3. Arne Risa Hole & Hong Il Yoo, 2017. "The use of heuristic optimization algorithms to facilitate maximum simulated likelihood estimation of random parameter logit models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 997-1013, November.

    More about this item

    Keywords

    Optimisation heuristics; Robust Regression; Least Median of Squares;

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