Applicability evaluation of Akaike’s Bayesian information criterion to covariance modeling in the cross-section adjustment method

Abstract

The applicability of Akaike’s Bayesian Information Criterion (ABIC) to the covariance modeling in the cross-section adjustment method has been investigated. In the conventional cross-section adjustment method, the covariance matrices are assumed to be true. However, this assumption is not always appropriate. To improve the reliability of the cross-section adjustment method, the estimation of the covariance model using the metric ABIC has been introduced, and the performance of ABIC has been investigated through simple numerical experiments. This paper derives the formula to efficiently evaluate ABIC which is represented by a lower rank matrix to enable numerical experiments with large samples in a realistic computation time. From the results of the numerical experiments, it has been confirmed that ABIC tends to select a covariance model with fewer hyperparameters and a smaller variance for the estimation error. However, it has also been found that this desirable property of ABIC will be lost when the structure of the covariance model is far from the true one.