  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 count-valued multivariate
time series. We develop a computationally-intensive algorithm that performs the
estimation by aggregating support sets obtained by applying the LASSO to data
subsamples. Our approach is to identify several well-fitting candidate models
and estimate S by the most frequently-used parameters, thus
\textit{aggregating} candidate models rather than selecting a single candidate
deemed optimal in some sense. While our method is broadly applicable to any
selection problem, we focus on the generalized vector autoregressive model
class, and in particular the Poisson case, due to (i) the difficulty of the
support estimation problem due to complex dependence in the data, (ii) recent
work applying the LASSO in this context, and (iii) interesting applications in
network recovery from discrete multivariate time series. We establish benchmark
methods based on the LASSO and present empirical results demonstrating the
superior performance of our method. Additionally, we present an application
estimating ecological interaction networks from paleoclimatology data.
