High Dimensional and Banded Vector Autoregressions

By Shaojun Guo, Yazhen Wang, Qiwei Yao. 2015

78 citations recorded by the source corpus.

We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The structure is also practically meaningful when the order of component time series is arranged appropriately. The convergence rates for the estimated banded autoregressive coefficient matrices are established. 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 structure for the auto-covariance functions of banded vector autoregressive processes, consistent estimators for the auto-covariance matrices are constructed.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59f0634752b2b07fc5e2202ec8e9f37c2e4a5535

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jinyuan Chang
2. Rong Chen
3. Clifford Lam
4. Qiwei Yao
5. Zeng Li
6. Bin Guo
7. Jianfeng Yao
8. Han Xiao

In Finance

1. Clifford Lam
2. Jinyuan Chang
3. Bin Guo
4. Rong Chen
5. Qiwei Yao
6. Han Xiao
7. Dan Yang
8. Zeng Li

In Statistics and Probability

1. Jinyuan Chang
2. Rong Chen
3. Qiwei Yao
4. Clifford Lam
5. Zeng Li
6. Bin Guo
7. Jianfeng Yao
8. Han Xiao

Citations in the corpus

• On testing for high-dimensional white noise (2018, methodology): “When the dimension is large, most existing works regularize the fitted models by Lasso [6, 17, 19, 32], Dantzig penalization [16], banded autocovariances [7], or banded auto-coefficient matrices [13].”
• Principal component analysis for second-order stationary vector time series (2014, methodology): “Under different sparsity assumptions, VAR models have been estimated by LASSO regularization (Shojaie and Michailidis, 2010; Song and Bickel, 2011), or by the Dantzig selector (Han and Liu, 2013). Guo, Wang and Yao (2016) considered high-dimensional autoregression with banded coefficient matrices. T”
• Autoregressive models for matrix-valued time series (2018, background): “…these works fall into two major categories: (i) vector autoregressive modeling with regularization (Davis et al., 2012; Basu and Michailidis, 2015; Guo et al., 2015; Han et al., 2015, 2016; Nicholson et al., 2015; Song and Bickel, 2011; Kock and Callot, 2015; Negahban and Wainwright, 2011; Nardi…”