High-Dimensional Granger Causality Tests with an Application to VIX and News
High-Dimensional Granger Causality Tests with an Application to VIX and News
This paper develops a framework for Granger causality testing in high-dimensional time series using regularized regressions, specifically the sparse-group LASSO (sg-LASSO). The authors establish a debiased central limit theorem for low-dimensional groups of coefficients, enabling inference on individual coefficients and groups. They also prove consistency of the HAC estimator for the long-run variance based on sg-LASSO residuals, showing that convergence rates depend on tail thickness and persistence. A new Fuk-Nagaev inequality for τ-mixing processes with polynomial tails is derived, which is crucial for handling heavy-tailed data. The methodology is applied to study Granger causality between the VIX and financial news, revealing that news topics Granger-cause VIX but not the reverse. The theoretical results are supported by Monte Carlo simulations.
Highlights
- 1Develops debiased central limit theorem for sparse-group LASSO with time series data, enabling valid inference for individual and groups of coefficients.
- 2Establishes HAC estimator consistency for sg-LASSO residuals in high-dimensional settings, with convergence rates affected by tail thickness and persistence.
- 3Proves a new Fuk-Nagaev inequality for τ-mixing processes with polynomial tails, of independent interest for heavy-tailed time series.
- 4Applies methodology to test Granger causality between VIX and financial news, demonstrating practical relevance.
Methods
- MSparse-group LASSO (sg-LASSO) regularization for high-dimensional time series with group structures.
- MNodewise LASSO for precision matrix estimation to debias sg-LASSO coefficients.
- MHeteroskedasticity and autocorrelation consistent (HAC) estimation of long-run variance using sg-LASSO residuals.
- MFuk-Nagaev inequality for τ-mixing processes to handle heavy-tailed and persistent data.
Results
- RDebiased sg-LASSO estimator converges to a normal distribution with explicit bias correction and long-run variance.
- RHAC estimator consistency requires bandwidth scaling with dimension, tail index, and persistence.
- RGranger causality tests are valid under high-dimensional settings with heavy-tailed and autocorrelated errors.
- REmpirical application finds significant Granger causality from financial news to VIX, but not vice versa.
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