Statistical Estimation of High-Dimensional Vector Autoregressive Models
This work addresses the challenge of fitting sparse VAR models in high-dimensional settings for time series analysis, representing an incremental improvement with a novel sparsity approach.
The paper tackles the problem of estimating high-dimensional vector autoregressive (VAR) models for multivariate time series by proposing a new sparsity scheme and showing that thresholding extends consistency properties to various matrix norms, enabling applications like forecasting and second-order characteristic estimation, with extensive simulations comparing regularized estimators.
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper 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 considered. Furthermore, it is shown that, under this sparsity setting, threholding extents 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 inference 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.