Time series regression analysis relies on the heteroskedasticity- and autocorrelation-consistent (HAC) estimation of the asymptotic variance to conduct proper inference. This paper develops such inferential methods for high-dimensional time series regressions . To recognize the time series data structures we focus on the sparse-group LASSO estimator  . We establish the debiased central limit theorem for low dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sparse-group LASSO residuals.  The treatment relies on a new Fuk-Nagaev inequality for a class of \tau -dependent processes with heavier than Gaussian tails, which is of independent interest  .
We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and develop the inferential theory in the high-dimensional setting . To recognize the time series data structures we focus on the sparse-group LASSO estimator , which includes the LASSO and the group LASSO as special cases . We establish the debiased central limit theorem for low dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sparse-group LASSO residuals. This leads to valid time series inference for individual regression coefficients as well as groups, including Granger causality tests. The treatment relies on a new Fuk-Nagaev inequality for a class of \tau -mixing processes with heavier than Gaussian tails, which is of independent interest . In an empirical application, we study the Granger causal relationship between the VIX and financial news .
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Time series regression analysis relies on the heteroskedasticity- and autocorrelation-consistent
We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent
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to conduct proper inference. This paper develops such inferential methods for
and develop the inferential theory in the
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time series regressions
setting
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, which includes the LASSO and the group LASSO as special cases
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This leads to valid time series inference for individual regression coefficients as well as groups, including Granger causality tests.
R
-dependent
-mixing
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. In an empirical application, we study the Granger causal relationship between the VIX and financial news