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Multivariate spatiotemporal models with low rank coefficient matrix

Dan Pu, Kuangnan Fang, Wei Lan, Jihai Yu and Qingzhao Zhang

Journal of Econometrics, 2024, vol. 246, issue 1

Abstract: Multivariate spatiotemporal data arise frequently in practical applications, often involving complex dependencies across cross-sectional units, time points and multivariate variables. In the literature, few studies jointly model the dependence in three dimensions. To simultaneously model the cross-sectional, dynamic and cross-variable dependence, we propose a multivariate reduced-rank spatiotemporal model. By imposing the low-rank assumption on the spatial influence matrix, the proposed model achieves substantial dimension reduction and has a nice interpretation, especially for financial data. Due to the innate endogeneity, we propose the quasi-maximum likelihood estimator (QMLE) to estimate the unknown parameters. A ridge-type ratio estimator is also developed to determine the rank of the spatial influence matrix. We establish the asymptotic distribution of the QMLE and the rank selection consistency of the ridge-type ratio estimator. The proposed methodology is further illustrated via extensive simulation studies and two applications to a stock market dataset and an air pollution dataset.

Keywords: Multivariate spatiotemporal model; Reduced-rank regression; Quasi-maximum likelihood estimation; Ridge-type ratio estimator (search for similar items in EconPapers)
JEL-codes: C31 C33 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:246:y:2024:i:1:s0304407624002483

DOI: 10.1016/j.jeconom.2024.105897

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