Ensemble and temporal parameter estimators are developed for linear and nonlinear stochastic differential equations driven by both Wiener and Poisson processes. Linear moment recursion relations are obtained for the stationary moments of the process. Consistency and asymptotic normality of the resulting ensemble estimators are demonstrated. The temporal estimators, i.e., using a single temporal record, are shown to coincide with maximum likelihood estimators in the special case of linear systems driven by Wiener noise. A simulation study illustrates the use of the ensemble and temporal estimators.