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TESTS FOR ROBUST VERSUS LEAST SQUARES FACTOR MODEL FITS

TESTS FOR ROBUST VERSUS LEAST SQUARES FACTOR MODEL FITS. R . Douglas Martin* Computational Finance Program Director Departments of Applied Mathematics and Statistics University of Washington doug@stat.washington.edu R-Finance 2014 May 16, 2014, Chicago

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TESTS FOR ROBUST VERSUS LEAST SQUARES FACTOR MODEL FITS

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  1. TESTS FOR ROBUST VERSUS LEAST SQUARES FACTOR MODEL FITS R. Douglas Martin* Computational Finance Program Director Departments of Applied Mathematics and Statistics University of Washington doug@stat.washington.edu R-Finance 2014 May 16, 2014, Chicago * Joint work with Tatiana Maravina (PhD, Boeing Company) and Kjell Konis, Department of Applied Mathematics University of Washington.

  2. Time Series Factor Models Robust M-Estimates UselmRobin package robust

  3. Favorite Rho and Psi Functions Optimal bias robust: Svarc, M., Yohai, V. J., & Zamar, R. H. (2002).

  4. Test Statistic T1 (Hausman-type) H1: Errors have a normal distribution K1: Errors have a symmetric or skewed non-normal distribution K2: Joint distribution of asset and factor returns is bias producing Efficient under H1 (see Hausman, 1978) Test Statistic T2 (Wald-type) H2: Errors have a normal distribution or a non-normal distribution K2: Joint distribution of asset and factor returns is bias producing

  5. R-Implementation New functions in package robust (Kjell Konis), to be submitted to CRAN by Sunday 5/18: lsRobTest > args(lsRobTest) function (object, test = c("T2", "T1"), ...) Object = an lmRob fitted model object

  6. > lsRobTest(fit.mm, test="T1") Test for least squares bias H0: normal regression error distribution Individual coefficient tests: LS Robust Delta Std. Error Stat p-value x 1.497 1.798 -0.3009 0.009612 -31.31 3.889e-215 > lsRobTest(fit.mm, test="T2") Test for least squares bias H0: composite normal/non-normal regression error distribution Individual coefficient tests: LS Robust Delta Std. Error Stat p-value x 1.497 1.798 -0.3009 0.08383 -3.589 0.0003315

  7. T1 p-value = .65 T2 p-values = .82

  8. References Bailer, Maravina and Martin (2011). “Robust betas in asset management”, Handbook of Quantitative Asset Management, Oxford University Press. Maravina and Martin (2014). “A Hausmantype test of robust versus least-squares regression fits”, submitted to SSRN on 5/18/2014. Maravina and Martin (2014). “A Wald type test of robust versus least-squares regression fits”, in preparation.

  9. Appendix: Test Statistics T1 and T2 T1: T2:

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