A2039
Title: Factor models of matrix-valued time series: Nonstationarity and cointegration
Authors: Degui Li - University of Macau (China)
Yayi Yan - Shanghai University of Finance and Economics (China) [presenting]
Qiwei Yao - London School of Economics (UK)
Abstract: A matrix factor model is proposed for nonstationary matrix-valued time series with common stochastic trends. Unlike traditional factor analysis, which flattens matrix observations into vectors, the matrix factor model fully explores the intrinsic matrix structure in the data, allowing interaction between row and column stochastic trends and subsequently improving estimation convergence while reducing computational complexity. The main estimation methodology is built on eigenanalysis of sample row and column covariance matrices when nonstationary matrix factors are of full rank and idiosyncratic components are temporally stationary, and is further extended to tackle more flexible settings when matrix factors are cointegrated and idiosyncratic components may be nonstationary. Under mild conditions allowing the existence of weak factors, convergence theory for estimated factor loading matrices and nonstationary factor matrices is derived. The developed methodology and theory are applicable to the general case of heterogeneous strengths over weak factors. An easy-to-implement ratio criterion is adopted to consistently estimate the size of the latent factor matrix. Simulation and empirical studies examine the numerical performance of the developed model and methodology in finite samples.
