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Abstract:
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High-dimensional auto-regressive models provide a natural way to model influence between M actors given multi-variate time series data for T time intervals. While there has been considerable work on network estimation, there is limited work in the context of inference and hypothesis testing. In particular, since most estimators such as the Lasso and Dantzig selectors are biased, certain de-biasing techniques are required. Existed results on hypothesis testing in time series has been restricted to linear Gaussian auto-regressive models, while it is practically important to determine suitable statistical tests for connections between actors that go beyond the Gaussian assumption. In this paper, we address these challenges and provide convergence in distribution results and confidence intervals for the multi-variate AR(p) model with sub-Gaussian noise, a generalization of Gaussian noise that broadens applicability and presents numerous technical challenges. The main technical challenge lies in the fact that unlike Gaussian random vectors, for sub-Gaussian vectors zero correlation does not imply independence. We validate our theoretical results with simulation results.
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