The influence of covariance Hankel matrix dimension on algorithms for VARMA models

Abstract

Some methods for estimating VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. Some authors suggest taking a larger dimension than theoretically necessary for this matrix. If the data sample is populous enough and the Hankel matrix dimension is unnecessarily large, this may result in an unnecessary number of computations, as well as in worse numerical and statistical results. We provide some theoretical results to know which is the Hankel matrix with the lowest dimension that is theoretically necessary and illustrate, with several simulated VARMA models, that using a dimension of the Hankel matrix greater than the theoretical minimal dimension proposed as valid does not necessarily lead to improved estimates. Although we use two algorithms, our main contributions are independent of the estimation method considered. We note that our paper does not include any comparisons between different algorithms for estimating VARMA models, as this is not our aim.