We develop an LM test for Granger causality in high-dimensional (HD) vector autoregressive (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. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in HD compared to standard low-dimensional VARs.

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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-doubleselection 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. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in high-dimensional compared to standard low-dimensional VARs.

<div> <div> <div> <p>We use the framework of Granger-causality testing in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global as well as hemispheric temperatures. By allowing for high dimensionality in the model we can enrich the information set with all relevant natural and anthropogenic forcing variables to obtain reliable causal relations. These variables have mostly been investigated in an aggregated form or in separate models in the previous literature. An additional advantage of our framework is that it allows to ignore the order of integration of the variables and to directly estimate the VAR in levels, therefore avoiding accumulating biases coming from unit-root and cointegration tests. This is of particular appeal for climate time series which are often argued to contain specific stochastic trends as well as yielding long memory. We are thus able to display the causal networks linking radiative forcings to global and hemispheric temperatures but also to causally connect radiative forcings among themselves, therefore allowing for a careful reconstruction of a timeline of causal effects among forcings. The robustness of our proposed procedure makes it an important tool for policy evaluation in tackling global climate change.</p> </div> </div> </div>

In the interactive effects panel data literature information criteria are commonly used to consistently determine which of the estimated principal components factors to include. The present paper shows that the same approach can be applied to factors estimated by taking the cross-sectional averages of the observables, as prescribed by the popular common correlated effects (CCE) approach. This should be useful to practitioners, because at the moment there is no other theory that justifies the use of information criteria in CCE.

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In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high dimensionality in the model we can enrich the information set with all relevant natural and anthropogenic forcing variables to obtain reliable causal relations. These variables have mostly been investigated in an aggregated form or in separate models in the previous literature. Additionally, our framework allows to ignore the order of integration of the variables and to directly estimate the VAR in levels, thus avoiding accumulating biases coming from unit-root and cointegration tests. This is of particular appeal for climate time series which are well known to contain stochastic trends as well as yielding long memory. We are thus able to display the causal networks linking radiative forcings to global temperatures but also to causally connect radiative forcings among themselves, therefore allowing for a careful reconstruction of a timeline of causal effects among forcings. The robustness of our proposed procedure makes it an important tool for policy evaluation in tackling global climate change.