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Granger Causality Testing in High-Dimensional VARs a Post-Double-Selection Procedure

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Document pages: 54 pages

Abstract: We develop an LM test for Granger causality in high-dimensional VAR modelsbased on penalized least squares estimations. To obtain a test retaining theappropriate size after the variable selection done by the lasso, we propose apost-double-selection procedure to partial out effects of nuisance variablesand establish its uniform asymptotic validity. We conduct an extensive set ofMonte-Carlo simulations that show our tests perform well under different datagenerating processes, even without sparsity. We apply our testing procedure tofind networks of volatility spillovers and we find evidence that causalrelationships become clearer in high-dimensional compared to standardlow-dimensional VARs.

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