Large-Vector Autoregression for Multilayer Spatially Correlated Time Series

One of the most commonly used methods for modeling multivariate time series is the vector autoregressive model (VAR). VAR is generally used to identify lead, lag, and contemporaneous relationships describing Granger causality within and between time series. In this article, we investigate the VAR methodology for analyzing data consisting of multilayer time series that are spatially interdependent. When modeling VAR relationships for such data, the dependence between time series is both a curse and a blessing. The former because it requires modeling the between time-series correlation or the contemporaneous relationships which may be challenging when using likelihood-based methods. The latter because the spatial correlation structure can be used to specify the lead–lag relationships within and between time series, within and between layers. To address these challenges, we propose an L₁L₂ regularized likelihood estimation method. The lead, lag, and contemporaneous relationships are estimated using an efficient algorithm that exploits sparsity in the VAR structure, accounts for the spatial dependence, and models the error dependence. We consider a case study to illustrate the applicability of our method. In the supplementary materials available online, we assess the performance of the proposed VAR model and compare it with existing methods within a simulation study.