ABSTRACT
This chapter explains a method for efficiently computing the log-likelihood of the autoregressive moving average model (ARMA) model based on the state-space representation and the Kalman filter. Applying the numerical optimization method, it is possible to maximize the log-likelihood. By this procedure, the maximum likelihood estimates of the parameters of the ARMA model can be obtained. The chapter considers two types of the state-space representation for an agressive model. The first is the natural representation for which the initial variance covariance matrix has a very simple form. The second respresentation is a special form of the state-space representation of an ARMA model, and the initial variance covariance matrix for this representation is generalized to an ARMA model.
