Finite sample effects in vector autoregressive modeling

In vector autoregressive modeling, the order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. Finite sample effects are an important cause of overfit. By incorporating finite sample effects, an order selection criterion for vector AR models can be found with an optimal trade-off of underfit and overfit. The finite sample formulae in this paper provide a more accurate description of the behavior of vector autoregressive estimators than asymptotic theory or the exact Cramér–Rao lower bound. A comparison of estimators in simulations as well as experimental data shows that the Nuttall–Strand estimator is more accurate than the least-squares estimator for high-order models. With the extension to channel prediction, the finite sample theory can also be used in order selection for autoregressive models with exogeneous input (ARX models) in system identification.