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

Abstract

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.

Forecasting Cryptocurrencies Log-Returns: a LASSO-VAR and Sentiment Approach

“…The randomness in the selection step means that post-selection estimators do not converge uniformly to a normal distribution, as the potential omitted variable bias from omitting weak, but still relevant, variables in the selection step is too large to perform uniformly valid inference. Many authors tried to cope with this issue (see Hecq et al (2019) for a comprehensive review). We adopt the procedure proposed by Hecq et al (2019) who specifically implemented a post-double-selection procedure, initially developed by Belloni et al (2014), in a VAR context.…”

“…Many authors tried to cope with this issue (see Hecq et al (2019) for a comprehensive review). We adopt the procedure proposed by Hecq et al (2019) who specifically implemented a post-double-selection procedure, initially developed by Belloni et al (2014), in a VAR context. The idea behind their approach is that Ξ is made of variables of interest, possible Granger-causing variables and the remaining variables.…”

Hierarchical Regularizers for Mixed-Frequency Vector Autoregressions

“…This curse of dimensionality has mostly been addressed through mixed-frequency factor models (e.g., Marcellino and Schumacher, 2010;Foroni and Marcellino, 2014;Andreou et al, 2019) or Bayesian estimation (e.g., Schorfheide and Song, 2015;McCracken et al, 2015;Ghysels, 2016;Götz et al, 2016). Sparsity-inducing convex regularizers form an appealing alternative (see Hastie et al, 2015 for an introduction), but despite their popularity in regression and standard VAR settings (e.g., Hsu et al, 2008;Basu et al, 2015;Callot et al, 2017;Derimer et al, 2018;Smeekes and Wijler, 2018;Barigozzi and Brownlees, 2019;Hecq et al, 2019), they have only been rarely explored as a tool for dimension reduction in mixed-frequency models.…”