Recursive estimation methods for time series models usually make use of recurrences for the vector of parameters, the model error and its derivatives with respect to the parameters, plus a recurrence for the Hessian of the model error. An alternative method is proposed in the case of an autoregressive-moving average model, where the Hessian is not updated but is replaced, at each time, by the inverse of the Fisher information matrix evaluated at the current parameter. The asymptotic properties, consistency and asymptotic normality, of the new estimator are obtained. Monte Carlo experiments indicate that the estimates may converge faster to the true values of the parameters than when the Hessian is updated. The paper is illustrated by an example on forecasting the speed of wind.