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.