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

Degui Li, Yayi Yan, Qiwei Yao

arXiv 15 Aug 2025 · Econometrics · 1 citations (OpenAlex)

arXiv:2508.11358 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chen \ Fan (2023) Statistical inference for high-dimensional matrix-variate factor models1.000133100%
2Wang et al (2019) Factor models for matrix-valued high-dimensional time series1.00073100%
3Bai (2004) Estimating cross-section common stochastic trends in nonstationary panel data1.00063100%
4Bai \ Ng (2004) A PANIC attack on unit roots and cointegration1.00063100%
5Barigozzi et al (2021) Large-dimensional dynamic factor models: Estimation of impulse-response functions with I(1) cointegrated factors1.00053100%
6Chen et al (2025) Inference in matrix-valued time series with common stochastic trends and multifactor error structure1.00053100%
7Freyaldenhoven (2022) Factor models with local factors—determining the number of relevant factors1.00053100%
8He et al (2023) One-way or two-way factor model for matrix sequences? Journal of Econometrics 235(2), 1981–20040.87452100%
9Ahn \ Horenstein (2013) Eigenvalue ratio test for the number of factors0.8435360%
10Bai \ Ng (2002) Determining the number of factors in approximate factor models0.84333100%

Showing the top 10 of 40 scored citations.