On a fast algorithm for the exact information matrix of a Gaussian ARMA time series
Guy Mélard, André Klein · IEEE Transactions on Signal Processing · 1994
The paper is devoted to a new algorithm for the computation of the exact Fisher information matrix of a Gaussian autoregressive-moving average time series. The number of operations is an order of magnitude smaller than the fastest existing procedure. The algorithm is based on a set of new recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters, combined with the Chandrasekhar recursions used in the evaluation of the likelihood function.>