Sparse Vector Autoregressive Modeling

TL;DR

This paper introduces a two-stage sparse VAR modeling approach that effectively reduces model complexity and improves interpretability for multivariate time series, demonstrated through simulations and real-world data applications.

Contribution

The paper proposes a novel two-stage method for fitting sparse VAR models using partial spectral coherence and BIC, enhancing model sparsity and interpretability.

Findings

The 2-stage approach effectively reduces the number of AR coefficients.

Simulation results show improved stability and interpretability.

Applied to real data, it identified meaningful temporal relationships.

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.