Multilevel matrix factor model

Abstract

Large scale matrix data has been widely discovered and continuously studied in various fields recently. We propose a multilevel matrix factor model considering the existence of multi level factor structure in matrix time series. This model incorporates both global factors influencing all matrix time series and local factors confined to impact specific matrix time series. Asymptotic properties are established to ensure the consistency of our procedure for estimating factor loading matrices. To demonstrate the finite-sample performance of our estimation, we present comprehensive simulation results. Finally, we apply our model to an empirical analysis of eight indexes, including return, trading volume, and trading value, across 200 stocks from ten distinct industries.