High-dimensional structure learning of sparse vector autoregressive models using fractional marginal pseudo-likelihood

Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the model increases. In this paper we adopt an approximate Bayesian approach to the learning problem by combining fractional marginal likelihood and pseudo-likelihood. We propose a novel method, PLVAR, that is both faster and produces more accurate estimates than the state-of-the-art methods based on penalized regression. We prove the consistency of the PLVAR estimator and demonstrate the attractive performance of the method on both simulated and real-world data.