Bootstrap based inference for sparse high-dimensional time series models

Fitting sparse models to high-dimensional time series is an important area of statistical inference. In this paper, we consider vector autoregressive and develop appropriate bootstrap methods infer properties such processes. Our methodology generates pseudo using a model-based procedure which involves estimated, sparsified version the underlying model. Inference performed so-called de-sparsified or de-biased estimators model parameters. We derive asymptotic distribution in context establish validity proposed for estimation and, appropriately modified, testing purposes. particular, focus on that large groups coefficients equal zero. theoretical results are complemented by simulations investigate finite sample performance proposed. A real-life data application also presented.