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We propose a new 2-stage procedure that relies on the elastic net penalty toestimate a network based on partial correlations when data are heavy-tailed.The new estimator allows to consider the lasso penalty as a special case. UsingMonte Carlo simulations, we test the performance on several underlying networkstructures and four different multivariate distributions: Gaussian, t-Studentwith 3 and 20 degrees of freedom and contaminated Gaussian. Simulation analysisshows that the 2-stage estimator performs best for heavy-tailed data and it isalso robust to distribution misspecification, both in terms of identificationof the sparsity patterns and numerical accuracy. Empirical results onreal-world data focus on the estimation of the European banking network duringthe Covid-19 pandemic. We show that the new estimator can provide interestinginsights both for the development of network indicators, such as networkstrength, to identify crisis periods and for the detection of banking networkproperties, such as centrality and level of interconnectedness, that might playa relevant role in setting up adequate risk management and mitigation tools.

A 2-stage elastic net algorithm for estimation of sparse networks with heavy tailed data