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Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model

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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).
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Suggested Citation

  • Peter Winker & Marianna Lyra & Chris Sharpe, 2011. "Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model," Computational Management Science, Springer, vol. 8(1), pages 103-123, April.
    • Handle: RePEc:spr:comgts:v:8:y:2011:i:1:p:103-123
    DOI: 10.1007/s10287-009-0103-x
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    1. Kontoghiorghes, Erricos & Van Dijk, Herman K. & Colubi, Ana, 2017. "Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 1(C), pages 1-1.
    2. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 671-690.
    3. I. Roko & M. Gilli, 2008. "Using economic and financial information for stock selection," Computational Management Science, Springer, vol. 5(4), pages 317-335, October.
    4. Winker, Peter & Maringer, Dietmar, 2004. "The Hidden Risks of Optimizing Bond Portfolios under VaR," Research Notes 13, Deutsche Bank Research.
    5. Huseyin Ince, 2006. "Non-Parametric Regression Methods," Computational Management Science, Springer, vol. 3(2), pages 161-174, April.
    6. Zaman, Asad & Rousseeuw, Peter J. & Orhan, Mehmet, 2001. "Econometric applications of high-breakdown robust regression techniques," Economics Letters, Elsevier, vol. 71(1), pages 1-8, April.
    7. Erricos J. Kontoghiorghes & Berç Rustem & Peter Winker (ed.), 2008. "Computational Methods in Financial Engineering," Springer Books, Springer, number 978-3-540-77958-2, December.
    8. 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.
    9. 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.
    10. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
    11. 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.
    12. Gilli, Manfred & Winker, Peter, 2007. "2nd Special Issue on Applications of Optimization Heuristics to Estimation and Modelling Problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 2-3, September.
    13. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    14. Manfred Gilli & Dietmar Maringer & Peter Winker, 2008. "Applications of Heuristics in Finance," International Handbooks on Information Systems, in: Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), Handbook on Information Technology in Finance, chapter 26, pages 635-653, Springer.
    15. Gunter Dueck & Peter Winker, 1992. "New concepts and algorithms for portfolio choice," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 8(3), pages 159-178, September.
    16. Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
    17. Chan, Louis K. C. & Lakonishok, Josef, 1992. "Robust Measurement of Beta Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 265-282, June.
    18. Rousseeuw, Peter J. & Wagner, Joachim, 1994. "Robust regression with a distributed intercept using least median of squares," Computational Statistics & Data Analysis, Elsevier, vol. 17(1), pages 65-76, January.
    19. Marc G. Genton & Elvezio Ronchetti, 2008. "Robust Prediction of Beta," Springer Books, in: Erricos J. Kontoghiorghes & Berç Rustem & Peter Winker (ed.), Computational Methods in Financial Engineering, pages 147-161, Springer.
    20. Krink, Thiemo & Paterlini, Sandra & Resti, Andrea, 2007. "Using differential evolution to improve the accuracy of bank rating systems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 68-87, September.
    21. Engel, Charles M & Rodrigues, Anthony P, 1993. "Tests of Mean-Variance Efficiency of International Equity Markets," Oxford Economic Papers, Oxford University Press, vol. 45(3), pages 403-421, July.
    22. 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.
    23. Peter Winker & Dietmar Maringer, 2009. "The convergence of estimators based on heuristics: theory and application to a GARCH model," Computational Statistics, Springer, vol. 24(3), pages 533-550, August.
    24. Katja Specht & Peter Winker, 2008. "Portfolio Optimization under VaR Constraints Based on Dynamic Estimates of the Variance-Covariance Matrix," Springer Books, in: Erricos J. Kontoghiorghes & Berç Rustem & Peter Winker (ed.), Computational Methods in Financial Engineering, pages 73-94, Springer.
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    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. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
    4. Manfred Gilli & Enrico Schumann, 2009. "Robust regression with optimisation heuristics," Working Papers 011, COMISEF.
    5. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    6. D. Blueschke & I. Savin, 2017. "No such thing as a perfect hammer: comparing different objective function specifications for optimal control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 377-392, June.
    7. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.
    8. Massimiliano Giacalone, 2022. "Optimal forecasting accuracy using Lp-norm combination," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 187-230, August.
    9. Ivan Savin & Dmitri Blueschke, 2013. "Solving nonlinear stochastic optimal control problems using evolutionary heuristic optimization," Jena Economics Research Papers 2013-051, Friedrich-Schiller-University Jena.
    10. Ivan Savin & Dmitri Blueschke, 2016. "Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 317-338, August.

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