Summary The second‐order dependence structure of purely non‐deterministic stationary processes is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process. This relationship together with some spectral density estimator is used to obtain consistent estimators of these coefficients. A spectral‐density‐driven bootstrap for time series is then developed which uses the entire sequence of estimated moving average coefficients together with appropriately generated pseudoinnovations to obtain a bootstrap pseudo‐time‐series. It is shown that if the underlying process is linear and if the pseudoinnovations are generated by means of an independent and identically distributed wild bootstrap which mimics, to the extent necessary, the moment structure of the true innovations, this bootstrap proposal asymptotically works for a wide range of statistics. The relationships of the proposed bootstrap procedure to some other bootstrap procedures, including the auto‐regressive sieve bootstrap, are discussed. It is shown that the latter is a special case of the spectral‐density‐driven bootstrap, if a parametric auto‐regressive spectral density estimator is used. Simulations investigate the performance of the new bootstrap procedure in finite sample situations. Furthermore, a real life data example is presented.

High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multi-variate time series. This article focuses on high-dimensional time series and on the different regularized estimation procedures proposed for fitting sparse VAR models to such time series. Attention is paid to the different sparsity assumptions imposed on the VAR parameters and how these sparsity assumptions are related to the particular consistency properties of the estimators established. A sparsity scheme for high-dimensional VAR models is proposed which is found to be more appropriate for the time series setting. Furthermore, it is shown that, under this sparsity setting, thresholding extends the consistency properties of regularized estimators to a wide range of matrix norms. Among other things, this enables application of the VAR parameters estimators to different problems, like forecasting or estimating the second-order characteristics of the underlying VAR process. Extensive simulations compare the finite sample behavior of the different regularized estimators proposed using a variety of performance criteria.

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The risk of obtaining MAIS 2+ injuries is significantly higher in oblique crashes than in nonoblique crashes. In the real world, most MAIS 2+ injuries occur in an oEES range from 30 to 60 km/h.

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