  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.
