Efficient bias robust regression for time series factor models

We introduce a robust regression estimator for time series factor models called the mOpt estimator. This estimator minimizes the maximum bias due to outlier generating distribution deviations from a standard normal errors distribution model, and at the same time has a high normal distribution efficiency. We demonstrate the efficacy of the mOpt estimator in comparison with the non-robust least squares (LS) estimator in applications to both single factor and multifactor time series models. For the case of single factor CAPM models we compared mOpt and LS estimates for cross sections of liquid stocks from the CRSP database in each contiguous two-year interval from 1963 to 1980. The results show that absolute differences between the two estimates greater than 0.3 occur for about 18% of the stocks, and differences greater than 0.5 occur for about 7.5% of the stocks. Our application of the mOpt estimator to multifactor models focuses on fitting the Fama-French 3-factor and the Fama-French-Carhart 4-factor models to weekly stock returns for the year 2008, using both the robust t-statistics associated with the mOpt estimates and a new statistical test for differences between the mOpt and LS coefficients. The results demonstrate the efficacy of the mOpt estimator in providing better model fits than the LS estimates, which are adversely influenced by outliers. Finally, since model selection is an important aspect of time series factor model fitting, we introduce a new robust prediction errors based model selection criterion called the Robust Final Prediction Error (RFPE), which makes natural use of the mOpt regression estimator. When applied to the 4-factor model, the RFPE finds as the best subset model the one that contains the Market, SMB and MOM factors, not the three Fama-French factors Market, SMB and HML. We anticipate that RFPE will prove to be quite useful for model selection of time series factor models.