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

Peter Winker, Marianna Lyra and Chris Sharpe

No 6, Working Papers from COMISEF

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).

Keywords: LMS; CAPM; Multi Factor Model; Differential Evolution; Threshold Accepting (search for similar items in EconPapers)
Pages: 22 pages
Date: 2008-08-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model (2011)
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