Sparse Vector Autoregressive Modeling

Abstract

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 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 2-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects non-zero 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 2-stage approach is illustrated with simulation results. The 2-stage approach is also applied to two real data examples: the first is the Google Flu Trends data and the second is a time series of concentration levels of air pollutants.

39 pages, 7 figures

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• Fitting Graphical Interaction Models to Multivariate Time Series
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• Principal component analysis for second-order stationary vector time series
• BigVAR: Tools for Modeling Sparse High-Dimensional Multivariate Time Series
• High-Dimensional Multivariate Time Series With Additional Structure
• Modeling High-Dimensional Unit-Root Time Series
• A Two-Way Transformed Factor Model for Matrix-Variate Time Series
• Autoregressive Models for Matrix-Valued Time Series
• Reduced-Rank Covariance Estimation in Vector Autoregressive Modeling
• A Structural-Factor Approach to Modeling High-Dimensional Time Series and Space-Time Data
• Segmenting High-dimensional Matrix-valued Time Series via Sequential Transformations