Robust Regression and its Application in Financial Data Analysis
This research is aimed to describe the application of robust regression and its advantages over the least square regression method in analyzing financial data. To do this, relationship between earning per share, book value of equity per share and share price as price model and earning per share, annual change of earning per share and return of stock as return model is discussed using both robust and least square regressions, and finally the outcomes are compared. Comparing the results from the robust regression and the least square regression shows that the former can provide the possibility of a better and more realistic analysis owing to eliminating or reducing the contribution of outliers and influential data. Therefore, robust regression is recommended for getting more precise results in financial data analysis.
[1] Azar, A. and Momeni,M., Business statistics, 3th Edition, Samt
Publications,Tehran, 2008.
[2] Anderson, D. R. and Sweeney, D. J, Statistics for Business and
Economics, 7th edition, Williams, T.A., South western college, 1998.
[3] Bamett, V. and Lewis. T, Outliers in Statistical data, Third ed., Wiley,
Chichester, 1993.
[4] Chatterjee, S. and Hadi A.S., Regression analysis by example, 4th
edition, Wiley, New Jersey, 2006.
[5] Chatterjee, S. and Hadi A.S., "Influential Observations, High Leverage
Points, and Outliers in Linear Regression", Statical Science, Vol. 1, No.
3, 1986, pp.379-416.
[6] Chatterjee, S. and Mächler, M., "Robust regression: A weighted least
squares approach", Communications in Statistics ÔÇö Theory and
Methods, No.26, 1997, pp.1381-1394.
[7] Chen, C., "Robust Regression and Outlier Detection with the
ROBUSTREG Procedure", presented at SUGI, No.27, 2002, pp.265.
[8] Cook, R. D., "Detection of influential observations in linear regression",
Technometrics, No. 19,1977, pp.15-18.
[9] Easton, P., & Harris. T., "Earnings as an Explanatory Variable for
Returns", Journal of Accounting Research, 1991, No.29, pp.19-36.
[10] Field, C. and Zhou, J., "Confidence intervals based on robust
regression", Journal of Statistical Planning and Inference, No.115, 2003,
pp.425 - 439.
[11] Gujarati, D.N., Basic Econometrics, Third edition, Mc Graw-Hill
international edition, 1995.
[12] Hoaglin,D.C. and Welsch,R.E., "The hat matrix in regressin and
ANOVA", The American Statistician, No.32, 1978, pp.17-22.
[13] Hodges J.L., Proc. Fifth Berkeley Symp. Math. Stat. Probab.,No.1, 1967,
pp.163-168. http: // www. 2sas . com / proceedings /sugi27/pdf.
[14] Liang,Y.Z. and Kvalheim O.M., "Robust methods for multivariate
analysis - a tutorial review", Chemometrics and Intelligent Laboratory
Systems, No.32, 1996, pp.1-10.
[15] Martin, R. D. "Robust Statistics with the S-Plus Robust Library and
Financial Applications", Vol. 1 and 2, Insightful Corp Presentation, New
York, NY, 2002, No.17-18.
[16] Neter, J. and Kunter, M. H., Nachtsheim, C. J. and Wasserman. W.,
Applied Linear Regression Models, Third edition, Mc Graw-Hill, USA,
1996.
[17] Ohlson, J., "Earnings, Book Values, and Dividends in Equity
Valuation", Contemporary Accounting Research, (Spring), 1995,
pp.661-687.
[18] Preminger, A. and Franck, R., "Forecasting exchange rates: A robust
regression approach", International Journal of Forecasting, No.23, 2007,
pp.71- 84.
[19] Rousseeuw P. J. and Zomeren B. C., "A comparison of some quick
algorithms for robust regression", Computational Statistics & Data
Analysis, Vol.14, 1992, pp.107-116.
[20] Rousseeuw, P.J. and Leroy, A.M., Robust Regression and Outlier
Detection, Wiley, New York, 1987.
[21] Rousseeuw, P.J. and Van Driessen, K., "Computing LTS Regression for
Large Data Sets", Technical Report, University of Antwerp, 1998.
[22] Rousseeuw, P.J., "Least Median of Squares Regression", Journal of the
American Statistical Association, No.79, 1984, pp. 871-880.
[23] Yaffee, R. A., "Robust Regression Analysis: Some Popular
Statistical Package Options", Statistics, Social Science, and Mapping
Group,Academic Computing Ser, 2002.
www.nyu.edu/its/socsci/docs/RobustReg2.pdf.
[1] Azar, A. and Momeni,M., Business statistics, 3th Edition, Samt
Publications,Tehran, 2008.
[2] Anderson, D. R. and Sweeney, D. J, Statistics for Business and
Economics, 7th edition, Williams, T.A., South western college, 1998.
[3] Bamett, V. and Lewis. T, Outliers in Statistical data, Third ed., Wiley,
Chichester, 1993.
[4] Chatterjee, S. and Hadi A.S., Regression analysis by example, 4th
edition, Wiley, New Jersey, 2006.
[5] Chatterjee, S. and Hadi A.S., "Influential Observations, High Leverage
Points, and Outliers in Linear Regression", Statical Science, Vol. 1, No.
3, 1986, pp.379-416.
[6] Chatterjee, S. and Mächler, M., "Robust regression: A weighted least
squares approach", Communications in Statistics ÔÇö Theory and
Methods, No.26, 1997, pp.1381-1394.
[7] Chen, C., "Robust Regression and Outlier Detection with the
ROBUSTREG Procedure", presented at SUGI, No.27, 2002, pp.265.
[8] Cook, R. D., "Detection of influential observations in linear regression",
Technometrics, No. 19,1977, pp.15-18.
[9] Easton, P., & Harris. T., "Earnings as an Explanatory Variable for
Returns", Journal of Accounting Research, 1991, No.29, pp.19-36.
[10] Field, C. and Zhou, J., "Confidence intervals based on robust
regression", Journal of Statistical Planning and Inference, No.115, 2003,
pp.425 - 439.
[11] Gujarati, D.N., Basic Econometrics, Third edition, Mc Graw-Hill
international edition, 1995.
[12] Hoaglin,D.C. and Welsch,R.E., "The hat matrix in regressin and
ANOVA", The American Statistician, No.32, 1978, pp.17-22.
[13] Hodges J.L., Proc. Fifth Berkeley Symp. Math. Stat. Probab.,No.1, 1967,
pp.163-168. http: // www. 2sas . com / proceedings /sugi27/pdf.
[14] Liang,Y.Z. and Kvalheim O.M., "Robust methods for multivariate
analysis - a tutorial review", Chemometrics and Intelligent Laboratory
Systems, No.32, 1996, pp.1-10.
[15] Martin, R. D. "Robust Statistics with the S-Plus Robust Library and
Financial Applications", Vol. 1 and 2, Insightful Corp Presentation, New
York, NY, 2002, No.17-18.
[16] Neter, J. and Kunter, M. H., Nachtsheim, C. J. and Wasserman. W.,
Applied Linear Regression Models, Third edition, Mc Graw-Hill, USA,
1996.
[17] Ohlson, J., "Earnings, Book Values, and Dividends in Equity
Valuation", Contemporary Accounting Research, (Spring), 1995,
pp.661-687.
[18] Preminger, A. and Franck, R., "Forecasting exchange rates: A robust
regression approach", International Journal of Forecasting, No.23, 2007,
pp.71- 84.
[19] Rousseeuw P. J. and Zomeren B. C., "A comparison of some quick
algorithms for robust regression", Computational Statistics & Data
Analysis, Vol.14, 1992, pp.107-116.
[20] Rousseeuw, P.J. and Leroy, A.M., Robust Regression and Outlier
Detection, Wiley, New York, 1987.
[21] Rousseeuw, P.J. and Van Driessen, K., "Computing LTS Regression for
Large Data Sets", Technical Report, University of Antwerp, 1998.
[22] Rousseeuw, P.J., "Least Median of Squares Regression", Journal of the
American Statistical Association, No.79, 1984, pp. 871-880.
[23] Yaffee, R. A., "Robust Regression Analysis: Some Popular
Statistical Package Options", Statistics, Social Science, and Mapping
Group,Academic Computing Ser, 2002.
www.nyu.edu/its/socsci/docs/RobustReg2.pdf.
@article{"International Journal of Business, Human and Social Sciences:64065", author = "Mansoor Momeni and Mahmoud Dehghan Nayeri and Ali Faal Ghayoumi and Hoda Ghorbani", title = "Robust Regression and its Application in Financial Data Analysis", abstract = "This research is aimed to describe the application of robust regression and its advantages over the least square regression method in analyzing financial data. To do this, relationship between earning per share, book value of equity per share and share price as price model and earning per share, annual change of earning per share and return of stock as return model is discussed using both robust and least square regressions, and finally the outcomes are compared. Comparing the results from the robust regression and the least square regression shows that the former can provide the possibility of a better and more realistic analysis owing to eliminating or reducing the contribution of outliers and influential data. Therefore, robust regression is recommended for getting more precise results in financial data analysis.
", keywords = "Financial data analysis, Influential data, Outliers,
Robust regression.", volume = "4", number = "11", pages = "2198-6", }
