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arXiv · 1912.09002

Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations

Ricardo P. Masini·Marcelo C. Medeiros·Eduardo F. Mendes
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Abstract

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. 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.

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Ricardo P. Masini, Marcelo C. Medeiros, Eduardo F. Mendes. 2019-12-19. Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations. https://arxiv.org/abs/1912.09002

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