Identification of a class of generalized autoregressive conditional heteroskedasticity (GARCH) models with applications to covariance propagation

Many practical problems require estimating future values of a Positive Definite matrix from past historical data. While several models have been proposed in the literature for propagating past data in this context, the problem of identifying these models from experiments is largely open. The main result of this paper is an efficient convex optimization based algorithm for identifying a class of models (GARCH) commonly used to propagate PSD matrices. A salient feature of the proposed approach is the fact that it minimizes a Riemannian measure of the estimation error, thus leading to better prediction results when compared against more naive algorithms based on minimizing Euclidian distances. These results are illustrated with a practical example arising in computer vision.