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

Abstract

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.

Cross-Sector Interactions in Western Europe: Lessons from Trade Credit Data

“…Therefore, to solve the model, it is necessary to achieve the correct balance between the required reduction in dimensions-to perform the estimations-and a reduction in the omitted-variable bias, to capture solely cross-sector interactions. This is the aim of Belloni et al's (2014) post-double-selection procedure, later developed by Hecq et al (2021) in a VAR framework for financial stock analysis. They developed a methodology to conduct conditional Granger-causality tests in high-dimensional frameworks, using two steps to balance the two imperatives.…”

“…This indicator is available on a monthly basis in the five countries at the sector level, without requiring the use of end-of-year balance-sheet data. I take advantage of a new high-dimensional VAR methodology developed by Hecq et al (2021) for financial stock analysis to balance between over-dimensionality issues and omitted-variable bias in the mapping process. Thanks to the use of the two-step method involving repeated lasso selections, I single out predictive relationships across sectors' financial conditions.…”

Lasso Inference for High-Dimensional Time Series

“…In a related approach, Javanmard and Montanari (2014), van de Geer et al (2014) and Zhang and Zhang (2014) introduce debiased or desparsified versions of the lasso that achieve uniform validity based on similar principles for IID Gaussian data. Extensions to the time series case include Chernozhukov et al (2019) who provide desparsified simultaneous inference on the parameters in a high-dimensional regression model allowing for temporal and cross-sectional dependency in covariates and error processes; Krampe et al (2018), who introduce bootstrap-based inference for autoregressive time series models based on the desparsification idea, and Hecq et al (2019) who use the post-double-selection procedure of Belloni et al (2014) for constructing uniformly valid Granger causality test in highdimensional VAR models.…”

Dimension Reduction for High Dimensional Vector Autoregressive Models

“…These methods can be gathered in two categories: the dimension reduction approach on the one hand and regularization techniques on the other hand. The latter group includes both Bayesian methods (Banbura et al, 2010), although Bayesian techniques are also used to estimate large reduced-rank VARs (see Carriero et al, 2011), and the more recent booming contributions on penalized estimation of sparse VARs (Wilms and Hecq et al, 2019). The former group of methods, to which our paper wishes to contribute, includes reduced rank techniques (Reinsel, 1983, Ahn and Reinsel, 1988, Carriero et al, 2011, Cubadda and Hecq, 2011, Bernardini and Cubadda, 2015 and the huge literature on factor models (surveyed in Bai and Ng, 2008.…”