Large Vector Auto Regressions for Multilayer Spatially Correlated Time Series

• Activity Number: 509
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rodrigue Ngueyep Tzoumpe*+ and Nicoleta Serban
• Companies: Georgia Institute of Technology and Georgia Institute of Technology
• Keywords: Multi-layer time series ; L1\L2 regularization ; spatially interdependent time series ; variable selection ; Vector Autoregressive Model ; Lasso

Abstract

The Vector Auto Regressive model can be used to identify lag and contemporaneous relationships for making inference on Granger causality within and between time series. Difficulties arise when the number of time series is large, when there is strong dependence between time series that are observations of different layers. We investigate methodology for analyzing data consisting of multi-layer time series which are spatially interdependent. The interdependence increases the difficulty because it requires modeling the between time series contemporaneous correlation which may be challenging when using likelihood-based methods. To address these challenges, we propose an L1\L2 regularized likelihood estimation method. We exploit the spatial dependence structure to specify the lag relationships between time series, within and between layers. The model is estimated using an efficient algorithm that exploits sparsity in the VAR structure,and models the error dependence. In a simulation study, we assess the estimation accuracy of the statistical model and demonstrate its superior performance over comparative methods. Real case studies are considered to show the applicability of our method.