P. Ginzberg and A. T. Walden, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 1, JANUARY 1, 2013, pp. 154-158. DOI: 10.1109/TSP.2012.2226170, http://www.researchgate.net/publication/258794004_Quaternion_VAR_Modelling_and_Estimation
Abstract — Quaternion vector autoregression (VAR) modeling is a natural extension of real and complex VAR. We demonstrate how a quaternion VAR can be treated as a special case of structured real VAR. We show that generalized least squares and (under Gaussianity) maximum likelihood estimation of the parameters reduces to simple least squares estimation if the innovations are quaternion proper.
Index Terms — Least squares, maximum likelihood, quaternions, vector autoregressive process.