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

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  • Ricardo P. Masini
  • Marcelo C. Medeiros
  • Eduardo F. Mendes

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. "Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations," Papers 1912.09002, arXiv.org, revised Jun 2021.
    • Handle: RePEc:arx:papers:1912.09002
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    Cited by:

    1. Robert Adamek & Stephan Smeekes & Ines Wilms, 2023. "Sparse High-Dimensional Vector Autoregressive Bootstrap," Papers 2302.01233, arXiv.org.
    2. Reuvers, Hanno & Wijler, Etienne, 2024. "Sparse generalized Yule–Walker estimation for large spatio-temporal autoregressions with an application to NO2 satellite data," Journal of Econometrics, Elsevier, vol. 239(1).
    3. Robert Adamek & Stephan Smeekes & Ines Wilms, 2024. "Local projection inference in high dimensions," The Econometrics Journal, Royal Economic Society, vol. 27(3), pages 323-342.
    4. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    5. Donggyu Kim & Minseog Oh, 2024. "Dynamic Realized Minimum Variance Portfolio Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1238-1249, October.
    6. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    7. Eugene Dettaa & Endong Wang, 2024. "Inference in High-Dimensional Linear Projections: Multi-Horizon Granger Causality and Network Connectedness," Papers 2410.04330, arXiv.org.

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