Projected estimation for large-dimensional matrix factor models

Long Yu, Yong He, Xinbing Kong and Xinsheng Zhang

Journal of Econometrics, 2022, vol. 229, issue 1, 201-217

Abstract: 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.

Keywords: Matrix factor model; Vector factor model; Column covariance matrix; Row covariance matrix (search for similar items in EconPapers)
JEL-codes: C23 C33 C38 C55 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:229:y:2022:i:1:p:201-217

DOI: 10.1016/j.jeconom.2021.04.001

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