Short-term forecasting with optimal transport

In this article, we leverage Optimal Transport theory to propose a novel nowcasting and short-term forecasting framework. Our methodology is designed to generate nowcasts for low-frequency variables by filling missing entries with values that optimally preserve the data distribution. To tackle this challenge, we introduce a loss function which is rooted in the Sinkhorn divergence. This loss function is formulated to embody the intuitive concept that two batches from the same dataset should exhibit identical distributions. We first showcase the performance of our approach as a stand-alone non-parametric framework. We further propose a parametric model where the Sinkhorn loss is adopted as an additional step that complements the Expectation-Maximization algorithm of a Dynamic Factor Model. Results of Monte Carlo simulations and of the empirical application to nowcast the US GDP show the superior performance of our proposal against suitable benchmark models.