In this paper we develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test which retains the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out the effects of the variables not of interest . We conduct an extensive set of Monte-Carlo simulations to compare different ways to set up the test procedure and choose the tuning parameter. The test performs well under different data generating processes, even when the underlying model is not very sparse. Additionally, we investigate two empirical applications : the money-income causality relation using a large macroeconomic dataset and networks of realized volatilities of a set of 49 stocks. In both applications we find evidences that the causal relationship becomes much clearer if a high-dimensional VAR is considered compared to a standard low-dimensional one .
We develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity . We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. In two applications on money and income and on volatility spillovers we find evidence that causal relationships become clearer in high-dimensional compared to standard low-dimensional VARs .
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which retains
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to compare different ways to set up the test procedure and choose the tuning parameter. The test performs
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when the underlying model is not very sparse. Additionally, we investigate two empirical applications : the money-income causality relation using a large macroeconomic dataset and networks of realized volatilities of a set of 49 stocks. In both applications we find evidences that the causal relationship becomes much clearer if a
without sparsity. In two applications on money and income and on volatility spillovers we find evidence that causal relationships become clearer in
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VAR is considered compared to a
compared to
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