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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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  • 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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    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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