We develop concentration inequalities for the lββ norm of a vector
linear processes on mixingale sequences with sub-Weibull tails. These
inequalities make use of the Beveridge-Nelson decomposition, which reduces the
problem to concentration for sup-norm of a vector-mixingale or its weighted
sum. This inequality is used to obtain a concentration bound for the maximum
entrywise norm of the lag-h autocovariance matrices of linear processes.
These results are useful for estimation bounds for high-dimensional
vector-autoregressive processes estimated using l1β regularisation,
high-dimensional Gaussian bootstrap for time series, and long-run covariance
matrix estimation