Exact Score for Time Series Models in State Space Form (Now published in Biometrika (1992), 79, 4, pp.283-6.)
Siem Jan Koopman and N.G. Shephard
The score vector for a time series model which fits into the Gaussian state space form can be approximated by numerically differentiating the log-likelihood. If the parameter vector is of length p, this involves the running of p + 1 Kalman filters. This paper shows the score vector can be computed in a single pass of the Kalman filter and a smoother. For many classes of models this dramatically increases the speed and reliability of algorithms for the numerical maximisation of likelihood.