A comparison of multivariate autoregressive estimators

Recently, a new estimator—Arfit—for multivariate (vector) autoregressive (MVAR) parameters has been proposed. Several other MVAR estimators (e.g. Levinson recursion, Burg-type Nuttall–Strand, etc.) were already well known in the field of signal processing.The various MVAR estimators have been implemented for Octave and Matlab. A method based on cross-validation and bootstrapping has been developed for comparing the various estimators. Thousand realizations of a MVAR(6)-process with 5 channels and a length of 1000 samples were generated. Each realization was separated into training and a test period. The training period was used to estimate the MVAR-parameters with each algorithm; the testing period was used to probe the accuracy of the estimates.For large sample sizes, the Burg-type algorithm and Arfit yielded similar results, the multivariate Levinson method was worse. For small sample sizes, the Burg-type Nuttall–Strand method was significantly better than multivariate Levinson, the Arfit estimates performed worst.In summary, the Nuttall–Strand method (multivariate Burg) for estimating MVAR parameters yielded the best results. The implementation of the algorithms for Octave and Matlab has been made available on the world wide web.