Evaluation of quadratic forms and traces for iterative estimation in first-order moving average models
T. W. Anderson, Raúl P. Mentz · Communication in Statistics- Theory and Methods · 1993
This paper deals with the evaluation of certain quadratic forms and traces associated with the irst-order moving average model. The problem arose while considering the maximum likelihood estimation under normality of the parameters of this model. The quadratic forms are y1R-jy, where y is a vector of observations generated by the models and R is the correlation matrix of the model; the traces are trR-j j cam be any natural number, but emphasis is placed on small Yalues, j = 1,2,3. Procedures in the time and frequency domains are studied, and the amount of computations needed in each case are considered and compared, from which a preferred approach emerges. The computations are compared with several alternative procedures suggested in the literature.