Multi-Process Models - An Application for the Construction of Financial Factor Models

Abstract

We present an unsupervised, comprehensive methodology for the construction of financial risk models. We o↵er qualitative comments on incremental functionality and quantitative measures of superior performance of compo-nent and mixture dynamic linear models rel-ative to alternative models. We apply our methodology to a high dimensional stream of daily closing prices for approximately 7,000 US traded stocks, ADRs, and ETFs for the most recent 10 years. Our methodology au-tomatically extracts an evolving set of ex-planatory time series from the data stream; maintains and updates parameter distribu-tions for component dynamic linear models as the explanatory time series evolve; and, ultimately specifies time-varying asset spe-cific mixture models. Our methodology uti-lizes a hierarchical Bayesian approach for the specification of component model parameter distributions and for the specification of the mixing weights in the final model. Our ap-proach is insensitive to the exact number of factors, and “e↵ectively ” sparse, as irrelevant factors (time series of pure noise) yield pos-terior parameter distributions with high den-sity around zero. The statistical models ob-tained serve a variety of purposes, including: outlier detection; portfolio construction; and risk forecasting. 1