Sparse factor model based on trend filtering

Abstract

We present a model based on trend filtering and regularization for performing factor analysis. Furthermore, the trend filtering method proposed in our model allows incorporating views represented as scenarios. Therefore, factor models can be optimized to explain not only trends of a given data series but also trends reflecting outlooks. As an application to finance, the proposed model constructs a sparse factor model on the trend of an index. Factor analyses on trend-filtered series provide factor models for describing trends, which are valuable for modeling long-term horizons. We also analyze the effect of trends on factor model selection in the US stock market. Further analyses include an investigation of factors during crisis periods and a comparison when various scenarios are considered.