Before revision:   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  .
After revision:  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 -dependent processes with heavier than Gaussian tails, which is of independent interest .