Sparse estimation of parameter support sets for generalized vector autoregressions by resampling and model aggregation

Abstract: The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series. We develop an algorithm that performs the estimation by aggregating support sets obtained by applying the LASSO to data subsamples. Our approach is to identify several candidate models and estimate S by selecting common parameters, thus "aggregating" candidate models. While our method is broadly applicable to any selection problem, we focus on the generalized vector autoregressive (GVAR) model class, and particularly the Poisson case, emphasizing applications in network recovery from discrete multivariate time series. We propose benchmark methods based on the LASSO, develop simulation strategies for GVAR processes, and present empirical results demonstrating the superior performance of our method. Additionally, we present an application estimating ecological interaction networks from paleoclimatology data.