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

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

doi:10.1111/jtsa.12627

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

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

Research output: Contribution to journal › Article › peer-review

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. 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 ((Formula presented.) -) mixing sequences as particular examples.

Original language	English (US)
Pages (from-to)	532-557
Number of pages	26
Journal	Journal of Time Series Analysis
Volume	43
Issue number	4
DOIs	https://doi.org/10.1111/jtsa.12627
State	Published - Jul 2022
Externally published	Yes

Keywords

high-dimensional time series
LASSO
mixing
VAR

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Online availability

10.1111/jtsa.12627

Library availability

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title = "Regularized estimation of high-dimensional vector autoregressions with weakly dependent innovations",

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. 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 ((Formula presented.) -) mixing sequences as particular examples.",

keywords = "high-dimensional time series, LASSO, mixing, VAR",

author = "Masini, {Ricardo P.} and Medeiros, {Marcelo C.} and Mendes, {Eduardo F.}",

note = "Funding Information: The authors are grateful to Anders B. Kock, Giuseppe Cavaliere, Etienne JJ Wijler, editor (Robert Taylor) and co-editor of JTSA, and two anonymous referees. Their comments and suggestions led to a much improved version of this manuscript. M. C. Medeiros acknowledges partial support from CNPq/Brazil and CAPES. Funding Information: The authors are grateful to Anders B. Kock, Giuseppe Cavaliere, Etienne JJ Wijler, editor (Robert Taylor) and co‐editor of JTSA, and two anonymous referees. Their comments and suggestions led to a much improved version of this manuscript. M. C. Medeiros acknowledges partial support from CNPq/Brazil and CAPES. Publisher Copyright: {\textcopyright} 2021 John Wiley & Sons Ltd.",

year = "2022",

month = jul,

doi = "10.1111/jtsa.12627",

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T1 - Regularized estimation of high-dimensional vector autoregressions with weakly dependent innovations

AU - Masini, Ricardo P.

AU - Medeiros, Marcelo C.

AU - Mendes, Eduardo F.

N1 - Funding Information: The authors are grateful to Anders B. Kock, Giuseppe Cavaliere, Etienne JJ Wijler, editor (Robert Taylor) and co-editor of JTSA, and two anonymous referees. Their comments and suggestions led to a much improved version of this manuscript. M. C. Medeiros acknowledges partial support from CNPq/Brazil and CAPES. Funding Information: The authors are grateful to Anders B. Kock, Giuseppe Cavaliere, Etienne JJ Wijler, editor (Robert Taylor) and co‐editor of JTSA, and two anonymous referees. Their comments and suggestions led to a much improved version of this manuscript. M. C. Medeiros acknowledges partial support from CNPq/Brazil and CAPES. Publisher Copyright: © 2021 John Wiley & Sons Ltd.

PY - 2022/7

Y1 - 2022/7

N2 - 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 ((Formula presented.) -) mixing sequences as particular examples.

AB - 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 ((Formula presented.) -) mixing sequences as particular examples.

KW - high-dimensional time series

KW - LASSO

KW - mixing

KW - VAR

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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