Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models
AbstractFor 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).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by COMISEF in its series Working Papers with number 006.
Length: 22 pages
Date of creation: 04 Aug 2008
Date of revision:
Contact details of provider:
Web page: http://www.comisef.eu
LMS; CAPM; Multi Factor Model; Differential Evolution; Threshold Accepting;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
- 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.
- Manfred GILLI & Peter WINKER, .
"A review of heuristic optimization methods in econometrics,"
Swiss Finance Institute Research Paper Series
08-12, Swiss Finance Institute.
- Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
- 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.
- Björn Fastrich & Peter Winker, 2010.
"Robust Portfolio Optimization with a Hybrid Heuristic Algorithm,"
- Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.
- Manfred Gilli & Enrico Schumann, 2009. "Robust regression with optimisation heuristics," Working Papers 011, COMISEF.
- Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Anil Khuman).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.