Title :
Quaternion VAR Modelling and Estimation
Author :
Ginzberg, P. ; Walden, A. T.
Author_Institution :
Department of Mathematics, Imperial College London, London, UK
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.
Keywords :
Biological system modeling; Covariance matrix; Least squares approximation; Quaternions; Reactive power; Technological innovation; Vectors; Least squares; maximum likelihood; quaternions; vector autoregressive process;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2226170