期刊
BIOMETRIKA
卷 103, 期 4, 页码 889-903出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asw046
关键词
Banded auto-coefficient matrix; Bayesian information criterion; Frobenius norm; Vector autoregressive model
资金
- Natural National Science Foundation of China
- U.S. National Science Foundation
- U.K. Engineering and Physical Sciences Research Council
- EPSRC [EP/L01226X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/L01226X/1] Funding Source: researchfish
We consider a class of vector autoregressive models with banded coefficient matrices. This setting represents a type of sparse structure for high-dimensional time series, although the implied auto-covariance matrices are not banded. The structure is also practically meaningful when the component time series are ordered appropriately. We establish the convergence rates of the estimated banded autoregressive coefficient matrices. We also propose a Bayesian information criterion for determining the width of the bands in the coefficient matrices, which is proved to be consistent. By exploring some approximate banded structures for the auto-covariance functions of banded vector autoregressive processes, consistent estimators for the auto-covariance matrices are constructed.
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