Sparse, Low-bias, and Scalable Estimation of High Dimensional Vector Autoregressive Models via Union of Intersections

Vector autoregressive (VAR) models are widely used for causal discovery and forecasting in multivariate time series analyses in fields as diverse as neuroscience, environmental science, and econometrics. In the high-dimensional setting, model parameters are typically estimated by L1-regularized maximum likelihood; yet, when applied to VAR models, this technique produces a sizable trade-off between sparsity and bias with the choice of the regularization hyperparameter, and thus between causal discovery and prediction. That is, low-bias estimation entails dense parameter selection, and sparse selection entails increased bias; the former is useful in forecasting but less likely to yield scientific insight leading to discovery of causal influences, and conversely for the latter. This paper presents a scalable algorithm for simultaneous low-bias and low-variance estimation (hence good prediction) with sparse selection for high-dimensional VAR models. The method leverages the recently developed Union of Intersections (UoI) algorithmic framework for flexible, modular, and scalable feature selection and estimation that allows control of false discovery and false omission in feature selection while maintaining low bias and low variance. This paper demonstrates the superior performance of the UoI-VAR algorithm compared with other methods in simulation studies, exhibits its application in data analysis, and illustrates its good algorithmic scalability in multi-node distributed memory implementations.