Before revision:  Most of the work is limited to either independent and identically distributed setting, or time series with independent and/or (sub-)Gaussian innovations . We extend current literatureto a broader set of innovation processes, by assuming that the error process is non-sub-Gaussian and conditionally heteroscedastic, and the generating process is not necessarily sparse. This setting covers fat tailed, conditionally dependent innovations which is of particular interest for financial risk modeling. It covers several multivariate-GARCH specifications, such as the BEKK model, and other factor stochastic volatility specifications  .
After revision:  In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an L^1 mixingale type condition on the centered conditional covariance matrices. This condition covers L^1-NED sequences and strong (\alpha-) mixing sequences as particular examples. From a modeling perspective, it covers several multivariate-GARCH specifications, such as the BEKK model, and other factor stochastic volatility specifications .