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Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models

Author

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  • Peter Winker
  • Marianna Lyra
  • Chris Sharpe

Abstract

For estimating the parameters of models for financial market data, the use of robust techniques is of particular interest. Conditional forecasts, based on the capital asset pricing model, and a factor model are considered. It is proposed to consider least median of squares estimators as one possible alternative to ordinary least squares. Given the complexity of the objective function for the least median of squares estimator, the estimates are obtained by means of optimization heuristics. The performance of two heuristics is compared, namely differential evolution and threshold accepting. It is shown that these methods are well suited to obtain least median of squares estimators for real world problems. Furthermore, it is analyzed to what extent parameter estimates and conditional forecasts differ between the two estimators. The empirical analysis considers daily and monthly data on some stocks from the Dow Jones Industrial Average Index (DJIA).

Suggested Citation

  • 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.
  • Handle: RePEc:com:wpaper:006
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    References listed on IDEAS

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    1. Yang, Zheng & Tian, Zheng & Yuan, Zixia, 2007. "GSA-based maximum likelihood estimation for threshold vector error correction model," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 109-120, September.
    2. Winker, Peter & Gilli, Manfred, 2004. "Applications of optimization heuristics to estimation and modelling problems," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 211-223, September.
    3. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    4. Manfred GILLI & Peter WINKER, "undated". "A review of heuristic optimization methods in econometrics," Swiss Finance Institute Research Paper Series 08-12, Swiss Finance Institute.
    5. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
    6. Barreto, Humberto & Maharry, David, 2006. "Least median of squares and regression through the origin," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1391-1397, March.
    7. Chan, Louis K. C. & Lakonishok, Josef, 1992. "Robust Measurement of Beta Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(02), pages 265-282, June.
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    Cited by:

    1. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.
    2. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.
    3. Manfred Gilli & Enrico Schumann, 2009. "Robust regression with optimisation heuristics," Working Papers 011, COMISEF.

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