Robust Time Series Factor Models

27 Pages Posted: 16 Aug 2021

See all articles by R. Douglas Martin

R. Douglas Martin

University of Washington

Daniel Xia

affiliation not provided to SSRN; Independent Researcher

Date Written: August 13, 2021


Abstract 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 factor model, and at the same time has a high normal distribution efficiency. The efficacy of this estimator is demonstrated in applications to single factor and multifactor time series models. Extensive empirical investigation of the mOpt robust betas versus non-robust least square betas show that 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. We introduce and demonstrate the use of a robust statistical test for differences between mOpt and least squares factor model coefficients, and also a new robust model selection method that makes natural use of the mOpt regression estimator. It is highly recommend that practitioners and data service providers compute robust mOpt betas as a standard practice complement to least squares betas.

Keywords: Robust regression, time-series factor models, bias, variance, efficiency

JEL Classification: C13, C61

Suggested Citation

Martin, R. Douglas and Xia, Daniel and Xia, Daniel, Robust Time Series Factor Models (August 13, 2021). Available at SSRN: or

R. Douglas Martin (Contact Author)

University of Washington ( email )

Applied Mathematics & Statistics
Seattle, WA 98195
United States

Daniel Xia

Independent Researcher ( email )

affiliation not provided to SSRN

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