Matrix-Factor-Augmented Regression

As matrix-variate observations are increasingly available, to incorporate the interplay between the multi-cross-sections, we introduce a matrix-factor-augmented regression model (M-FARM) that proposes to predict ahead of time with factors of matrix predictors augmented in the regression. We show that the estimation error in the factor matrices, estimated by the projection procedure in the first step, enters into the estimation error of the regression parameters and the prediction error of the response variable with an asymptotically negligible rate. The central limit theorems of the estimates of the regression parameters are established under some mild conditions. Forecasting intervals with a theoretical guarantee are given. Monte Carlo simulations justify the theoretical results. We find empirically that the augmented matrix factors do help in forecasting macroeconomic variables relative to the benchmark matrix autoregressive model and vector-factor-augmented regression model (V-FARM).