In this section different methods of estimating the ARMA parameters are presented: the Yule-Walker method, the Levinson-Durbin algorithm, Burg's algorithm, the innovations algorithm, the long AR method, the Hannan-Rissanen procedure, the maximum likelihood method, and the conditional maximum likelihood method. Functions calculating the logarithm of the likelihood function, the estimated information matrix, and the asymptotic covariance of the maximum likelihood estimators are also given. Residuals and the portmanteau statistic used in the diagnostic checking can also be obtained with functions defined in this section.