Sparse Vector Autoregressive Modeling

By Richard A. Davis, P. Zang, Tian Zheng. 2012

223 citations recorded by the source corpus.

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of the AR coefficients can be prohibitively large, resulting in noisy estimates, unstable predictions, and difficult-to-interpret temporal dependence. To overcome such drawbacks, we propose a two-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects nonzero AR coefficients based on an estimate of the partial spectral coherence (PSC) together with the use of BIC. The PSC is useful for quantifying the conditional relationship between marginal series in a multivariate process. A refinement second stage is then applied to further reduce the number of parameters. The performance of this two-stage approach is illustrated with simulation and real data examples. Supplementary materials for this article are available online.

Subfields: Analytical Chemistry, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ba7377ae6de455c087c797d6759eb10f10dcddc3

How researchers see this paper

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

In Analytical Chemistry

In Finance

In Statistics and Probability

Citations in the corpus

NETS: Network estimation for time series (2019, unknown): “Note that the notion of sparsity used in this work is different from that used in other papers such as Davis, Zang, and Zheng (2016), Kock and Callot (2015), and Medeiros and Mendes (2016), where sparsity assumptions are formulated for the autoregressive matrices only.”
A network analysis of the volatility of high dimensional financial series (2017, methodology): “…n data sets, is based on sparsity assumptions allowing for the application of penalized regression techniques (Hsu et al., 2008; Abegaz and Wit, 2013; Nicholson et al., 2014; Basu and Michailidis, 2015; Davis et al., 2015; Kock and Callot, 2015; Barigozzi and Brownless, 2016; Gelper et al., 2016).”
Identifying demand effects in a large network of product categories (2015, methodology): “Davis et al. (2012) propose another sparse estimation procedure for the VAR.”
Autoregressive models for matrix-valued time series (2018, background): “Roughly speaking 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…”
Granger Causality: A Review and Recent Advances (2021, methodology): “The general estimation framework in (8) has been extended to account for dependencies in the inverse covariance of the innovations, Σ − 1 (Davis et al., 2016), and to to combine the ideas of sparsity and unobserved exogenous variables (Basu et al., 2019).”
Random Forests for dependent data (2020, methodology): “VAR models enforce parsimony via graphical models [18].”