Banded spatio-temporal autoregressions

Abstract

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for highdimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and therefore, the proposal is radically different from the existing literature on the inference for high-dimensional banded covariance matrices. Due to the innate endogeneity, we apply the least squares method based on a Yule-Walker equation to estimate autoregressive coefficient matrices. The estimators based on multiple Yule-Walker equations are also studied. A ratio-based method for determining the bandwidth of autoregressive matrices is also proposed. Some asymptotic properties of the inference methods are established. The proposed methodology is further illustrated using both simulated and real data sets.

Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data

“…Each spatial unit in this application corresponds to an aggegration of a small number of pixels on the satellite image. We find that SPLASH constructs more accurate one-step ahead predictions for all spatial units compared to the procedure in Gao et al (2019), while outperforming a competitive penalized VAR benchmark for the majority of spatial units. In addition, we find evidence for spatial interactions between first-order neighbours and second-order neighbours (i.e.…”

“…Most closely related to the work presented in this paper are Gao et al (2019), andMa et al (2021). Both of these paper consider the same model and an estimation procedure that relies on the generalized Yule-Walker equations.…”

“…We propose the SPatial LAsso-type SHrinkage (SPLASH) estimator. Building upon previous works by Dou et al (2016) and Gao et al (2019), we study spatio-temporal regressions. Apart from a more generous bandwidth upper bound, this SPLASH estimator leaves the spatial weight matrix and autoregressive matrix unspecified while employing a lasso approach to recover sparse solutions.…”

Factor analysis for high‐dimensional time series: Consistent estimation and efficient computation

“…On the other hand, Assumption 5 is not the weakest possible, which can be replaced by the 𝛼-mixing. Readers who are interested in the explicit relations of different types of mixing are referred to [11,20] for details.…”

Finite sample theory for high-dimensional functional/scalar time series with applications

“…In the context of functional time series, many standard univariate or low-dimensional time series methods have been recently adapted to the functional domain with theoretical properties explored from a standard asymptotic perspective, see, e.g., Bosq (2000); Bathia, Yao and Ziegelmann (2010); Hörmann and Kokoszka (2010); Panaretos and Tavakoli (2013); Aue, Norinho and Hörmann (2015); Hörmann, Kidziński and Kokoszka (2015); Pham and Panaretos (2018); Li, Robinson and Shang (2020) and reference therein. In the context of high-dimensional time series, some lower-dimensional structural assumptions are often incorporated on the model parameter space and different regularized estimation procedures have been developed for the respective learning tasks including, e.g., high-dimensional sparse linear regression (Basu and Michailidis, 2015;Wu and Wu, 2016;Han and Tsay, 2020) and high-dimensional sparse vector autoregression (Guo, Wang and Yao, 2016;Lin and Michailidis, 2017;Gao et al, 2019;Ghosh, Khare and Michailidis, 2019;Zhou and Raskutti, 2019;Wong, Li and Tewari, 2020;Lin and Michailidis, 2020).…”