Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations

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‐...

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Bibliographic Details
Published inJournal of time series analysis Vol. 43; no. 4; pp. 532 - 557
Main Authors Masini, Ricardo P., Medeiros, Marcelo C., Mendes, Eduardo F.
Format Journal Article
LanguageEnglish
Published Oxford, UK John Wiley & Sons, Ltd 01.07.2022
Blackwell Publishing Ltd
Subjects
Autoregressive models
Covariance matrix
high‐dimensional time series
Innovations
LASSO
Matrices
mixing
Regularization
Sequences
Time series
VAR
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Summary: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. In contrast to current literature, our innovation process satisfy an L1 mixingale type condition on the centered conditional covariance matrices. This condition covers L1‐NED sequences and strong (α‐) mixing sequences as particular examples.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12627