High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting

Abstract: This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression linking future outcomes to these factors, estimated via iterative least squares. To handle weak factor structures, we introduce a supervised screening step to select informative rows and columns. Theoretical properties, including consistency and asymptotic normality, are established. Simulations and real data show that our method significantly improves forecast accuracy, with the screening procedure providing additional gains over standard benchmarks in out-of-sample mean squared forecast error.