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

Research output: Working paperProfessional

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Abstract

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.
Original languageEnglish
PublisherarXiv.org at Cornell University Library
Publication statusPublished - 28 Feb 2019

Keywords

  • Granger causality
  • post-double-selection
  • vector autoregressive models
  • high-dimensional inference

Cite this

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abstract = "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.",
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Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure. / Hecq, Alain; Margaritella, Luca; Smeekes, Stephan.

arXiv.org at Cornell University Library, 2019.

Research output: Working paperProfessional

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N2 - 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.

AB - 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.

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