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Robust regression with optimisation heuristics

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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.

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File URL: http://comisef.eu/files/wps011.pdf
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Bibliographic Info

Paper provided by COMISEF in its series Working Papers with number 011.

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Length: 26 pages
Date of creation: 08 Jul 2009
Date of revision:
Handle: RePEc:com:wpaper:011

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Web page: http://www.comisef.eu

Related research

Keywords: Optimisation heuristics; Robust Regression; Least Median of Squares;

This paper has been announced in the following NEP Reports:

References

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  1. 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 1355-82, September.
  2. Manfred GILLI & Enrico SCHUMANN, 2009. "An Empirical Analysis of Alternative Portfolio Selection Criteria," Swiss Finance Institute Research Paper Series 09-06, Swiss Finance Institute.
  3. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
  4. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
  5. 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.
  6. Blume, Marshall E, 1971. "On the Assessment of Risk," Journal of Finance, American Finance Association, vol. 26(1), pages 1-10, March.
  7. Manfred Gilli & Evis Këllezi & Hilda Hysi, . "A Data-Driven Optimization Heuristic for Downside Risk Minimization," Swiss Finance Institute Research Paper Series 06-02, Swiss Finance Institute.
  8. 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.
  9. 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.
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