Inference on matrix-valued factor models under a fixed time horizon

This paper considers the estimation and inference of matrix-valued factor models under a fixed time horizon. We show that the 2dPCA method maintains consistency and asymptotic normality. However, the conventional Newey-West method becomes infeasible, posing challenges for making inference. To address this limitation, we introduce an augmented CS-HAC estimator for computing the standard errors. Applying this method to a large set of county-industry level economic indicators, we identify an aggregate factor, a public sector factor, and a leisure and hospitality factor, and show how they are affected differently during the financial crisis and the COVID-19 pandemic.