Statistics and Its Interface

Volume 13 (2020)

Number 2

A spatial autoregression model with time-varying coefficients

Pages: 261 – 270

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n2.a10

Authors

Ke Xu (School of Statistics, University of International Business and Economics, Beijing, China)

Luping Sun (School of Business, Central University of Finance and Economics, Beijing, China)

Jin Liu (Guanghua School of Management, Peking University, Beijing, China)

Xuening Zhu (School of Data Science, Fudan University, Shanghai, China)

Hansheng Wang (Guanghua School of Management, Peking University, Beijing, China)

Abstract

This article proposes a spatial autoregression (SAR) model with time-varying coefficients. The model incorporates both spatial dependence and the impacts of explanatory variables, and all the coefficients are allowed to flexibly vary according to time. This article further develops a kernel-smoothed estimator (KSE) to estimate the time-varying coefficients. Compared with the maximum likelihood estimator (MLE) obtained at discrete time points, the KSE utilizes the potentially useful information from time neighborhoods. We have theoretically proved the consistency of the proposed KSE. A number of simulation studies show that the KSE is more accurate and performs substantially better than the MLE. Moreover, a real data analysis for a ride-hailing platform in China also shows that the KSE is more stable and interpretable. The proposed model as well as the KSE can be widely applied to data with a large number of cross-sectional units and regularly spaced time points.

Keywords

time-varying coefficients, spatial autoregression model, kernel-smoothed estimator, maximum likelihood estimator

Ke Xu, Jin Liu, and Hansheng Wang were supported by the National Natural Science Foundation of China (grant nos. 11525101, 71332006, and 71532001); and by China’s National Key Research Special Program (grant no. 2016YFC0207704).

Ke Xu was also supported by “the Fundamental Research Funds for the Central Universities” in UIBE (grant no. 19QD22).

Luping Sun was supported by National Natural Science Foundation of China (grant nos. 71972195 and 71502182); and by the Program for Innovation Research in Central University of Finance and Economics.

Xuening Zhu was supported by the National Natural Science Foundation of China (grant nos. 11901105, 71991472, 11971504, and U1811461); by the Shanghai Sailing Program for Youth Science and Technology Excellence (grant no. 19YF1402700); and by the Fudan-Xinzailing Joint Research Centre for Big Data, School of Data Science, Fudan University.