Identification of sparse multivariate autoregressive models

A heuristic search method is presented by which a multivariate auto-regressive (MVAR) process is identified such that its model order, sparse structure and noise covariance is accurately recovered. A novel minimum description length (MDL) formulation of time-series linear regression is derived and applied to the problem of identifying (and coding) sparse AR matrix structures such that sparsification is largely achieved in a single initial step and improved iteratively. The method was tested against synthetic data generated by known sparse MVAR processes, compared with commonly used model selection criteria (AIC, BIC) used for identification, suggesting that it is significantly more accurate and does not overfit.