Efficient Transport-based Estimation of Time-Varying Factor Models

The study of economic policies in the economy and financerequires efficient reduction of datasets into informative unobserved factors(UF) to account for agents' expectations and forecast future behavior.Principal Component Analysis (PCA) is a widely used statistical method for thispurpose. Recently the statistical and econometric literature is focusing on theimplication of the use of Optimal-Transport (OT) as a tool for implementing theprecision of data reduction when data are particularly complex. We discuss thepitfall of two nove PCA-based methods: NIPCA (Nonlinear Independent ComponentAnalysis) and Target PCA (T-PCA).  The former, despite its superiorcapability of fitting and reducing data under nonlinear representation, is computationally intensive. Moreover, it is based on a two-phase/hybridapproach. The latter, uses a linear factor structure with novel theoreticalcontributions relating the informativeness of datasets directly to the factors.However, it assumes informativeness, observability, and constancy of thefactors. We argue that a UF parametrization à la Mikkelsen et al. (2019)combined with modified NIPCA can address these problems. Namely, we propose analgorithm that combines Brenier mapping and diagonalization as a potentialsolution.