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

We present an unsupervised, comprehensive methodology for the construction of financial risk models. We offer qualitative comments on incremental functionality and quantitative measures of superior performance of component and mixture dynamic linear models relative 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 automatically extracts an evolving set of explanatory time series from the data stream; maintains and updates parameter distributions for component dynamic linear models as the explanatory time series evolve; and, ultimately specifies time-varying asset specific mixture models. Our methodology utilizes 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 approach is insensitive to the exact number of factors, and "effectively" sparse, as irrelevant factors (time series of pure noise) yield posterior parameter distributions with high density around zero. The statistical models obtained serve a variety of purposes, including: outlier detection; portfolio construction; and risk forecasting.