Vector Autoregressive Models with Spatially Structured Coefficients for Time Series on a Spatial Grid

• Activity Number: 497 - ENVR Student Paper Awards
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Yuan Yan* and Marc Genton and Hsin-Cheng Huang
• Companies: Dalhousie University and King Abdullah University of Science and Technology and Academia Sinica
• Keywords: Adaptive fused Lasso; Coefficients homogeneity; Penalized likelihood; Regularization; Spatial clusters; Spatiotemporal model

Abstract

We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data which may be collected at hundreds of locations, and capturing the spatial non-stationarity. In essence, our model is a vector autoregressive model that uses two levels of spatial structure to achieve parsimony of the matrix of autoregressive coefficients (transition matrix). The first level ensures the sparsity of the transition matrix and depends on the spatial proximity. The second level performs a spatial clustering of the non-zero autoregressive coefficients such that nearby locations share the same autoregressive coefficients. This model is interpretable and can be used to find spatial clusters. The parameter estimation in our model is obtained using the penalized log-likelihood with an adaptive fused Lasso penalty. Our model is appropriate for analyzing data collected on a space-time grid. We illustrate the performance of the proposed estimation algorithm in a simulation study and apply our model to daily wind speed time series generated from a climate model on an irregularly bounded grid over Saudi Arabia.