Alain Hecq, Luca Margaritella, Stephan Smeekes
arXiv 2 Feb 2023 · Econometrics
arXiv:2302.01434 · PDF · DOI · OpenAlex · Extracted main text
In this paper we construct an inferential procedure for Granger causality in high-dimensional non-stationary vector autoregressive (VAR) models. Our method does not require knowledge of the order of integration of the time series under consideration. We augment the VAR with at least as many lags as the suspected maximum order of integration, an approach which has been proven to be robust against the presence of unit roots in low dimensions. We prove that we can restrict the augmentation to only the variables of interest for the testing, thereby making the approach suitable for high dimensions. We combine this lag augmentation with a post-double-selection procedure in which a set of initial penalized regressions is performed to select the relevant variables for both the Granger causing and caused variables. We then establish uniform asymptotic normality of a second-stage regression involving only the selected variables. Finite sample simulations show good performance, an application to investigate the (predictive) causes and effects of economic uncertainty illustrates the need to allow for unknown orders of integration.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Toda, H. Y. and Yamamoto, T (1995) Statistical inference in vector autoregressions with possibly integrated processes | 0.928 | 5 | 4 | 80% |
| 2 | Belloni, A., Chernozhukov, V., and Hansen, C (2014) Inference on treatment effects after selection among high-dimensional controls | 0.928 | 4 | 3 | 100% |
| 3 | Dolado, J. J. and Lütkepohl, H (1996) Making wald tests work for cointegrated var systems | 0.737 | 3 | 2 | 100% |
| 4 | Hecq, A., Margaritella, L., and Smeekes, S (2021) Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure self | 0.737 | 3 | 2 | 100% |
| 5 | Adamek, R., Smeekes, S., and Wilms, I (2023) Lasso inference for high-dimensional time series self | 0.644 | 4 | 1 | 100% |
| 6 | Smeekes, S. and Wijler, E (2021) An automated approach towards sparse single-equation cointegration modelling self | 0.644 | 4 | 1 | 100% |
| 7 | Smeekes, S. and Wijler, E (2020) Unit roots and cointegration self | 0.644 | 2 | 2 | 100% |
| 8 | Smeekes, S. and Wilms, I (2023) bootur: An r package for bootstrap unit root tests self | 0.644 | 2 | 2 | 100% |
| 9 | Tibshirani, R (1996) Regression shrinkage and selection via the lasso | 0.644 | 2 | 2 | 100% |
| 10 | Baker, S. R., Bloom, N., and Davis, S. J (2016) Measuring economic policy uncertainty | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | High-Dimensional Granger Causality for Climatic Attribution | 1.000 | 7 | 3 |
| 2 | Sparse High-Dimensional Vector Autoregressive Bootstrap | 0.644 | 2 | 2 |
| 3 | Hierarchical Regularizers for Mixed-Frequency Vector Autoregressions | 0.405 | 1 | 1 |
| 4 | LASSO Inference for High Dimensional Predictive Regressions | 0.405 | 1 | 1 |