Neil Shephard The likelihood and score for autoregressive moving average models In this note I will study the relationship between the conditional sum of squares (CSS) estimator of moving averages and the maximum likelihood (ML) estimator. I will show that the CSS estimator can be converted into the ML estimator via the use of the EM algorithm. A by-product of the EM algorithm is an expression for the likelihood function and the score. This argument generalizes to autoregressive moving average (ARMA) models. The derivation of an analytic expression for the score for general ARMA models seems a new result.