Lasso inference for high-dimensional time series

In this paper we develop valid inference for high-dimensional time series. We extend the desparsified lasso to a series setting under Near-Epoch Dependence (NED) assumptions allowing non-Gaussian, serially correlated and heteroskedastic processes, where number of regressors can possibly grow faster than dimension. first derive an error bound weak sparsity, which, coupled with NED assumption, means inequality also be applied (inherently misspecified) nodewise regressions performed in lasso. This allows us establish uniform asymptotic normality general conditions, including on parameters increasing dimensions. Additionally, show consistency long-run variance estimator, thus providing complete set tools performing linear models. Finally, perform simulation exercise demonstrate small sample properties common settings.