Projected estimation for large-dimensional matrix factor models

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor...

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Veröffentlicht in:Journal of econometrics Jg. 229; H. 1; S. 201 - 217
Hauptverfasser: Yu, Long, He, Yong, Kong, Xinbing, Zhang, Xinsheng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.07.2022
Elsevier Sequoia S.A
Schlagworte:
Asymptotic methods
Column covariance matrix
Convergence
Economic factors
Eigenvalues
Estimating techniques
Estimation
Factor analysis
Finance
Grammatical aspect
Macroeconomics
Matrices
Matrix
Matrix factor model
Noise
Numerical analysis
Row covariance matrix
Signal to noise ratio
Vector factor model
C33
C55
C23
Column covariance matrix
C38
Vector factor model
Row covariance matrix
Matrix factor model
ISSN:0304-4076, 1872-6895
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Zusammenfassung:In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers. Extensive numerical studies verify the empirical performance of the projection method. Two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincide with financial, economic, or geographical interpretations.
Bibliographie:ObjectType-Article-1
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2021.04.001