Factor Models of Matrix-Valued Time Series: Nonstationarity and Cointegration

Degui Li (), Yayi Yan () and Qiwei Yao ()
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Degui Li: Faculty of Business Administration, Asia-Pacific Academy of Economics and Management, and Department of Economics, University of Macau
Yayi Yan: School of Statistics and Data Science, Shanghai University of Finance and Economics
Qiwei Yao: Department of Statistics, London School of Economics

No 202534, Working Papers from University of Macau, Faculty of Business Administration

Abstract: In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully explore the intrinsic matrix structure in the data, allowing interaction between the row and column stochastic trends, and subsequently improving the estimation convergence. It also reduces the computation complexity in estimation. The main estimation methodology is built on the eigenanalysis of sample row and column covariance matrices when the nonstationary matrix factors are of full rank and the idiosyncratic components are temporally stationary, and is further extended to tackle a more flexible setting when the matrix factors are cointegrated and the idiosyncratic components may be nonstationary. Under some mild conditions which allow the existence of weak factors, we derive the convergence theory for the estimated factor loading matrices and nonstationary factor matrices. In particular, 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 latent factor matrix. Both simulation and empirical studies are conducted to examine the numerical performance of the developed model and methodology in finite samples.

Keywords: common stochastic trends; eigenanalysis; matrix error-correction models; matrix factor models; ratio criterion (search for similar items in EconPapers)
Pages: 62 pages
Date: 2025-08
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