  Dynamic systems are ubiquitous in nature and are used to model many processes
in biology, chemistry, physics, medicine, and engineering. In particular,
systems of ordinary differential equations are commonly used for the
mathematical modelling of the rate of change of dynamic processes. In many
practical applications, the process can only be partially measured, a fact that
renders estimation of parameters of the system extremely challenging. Recently,
a 'direct integral estimator' for partially observed systems of ordinary
differential equations was introduced. The practical performance of the
integral estimator was demonstrated, but its theoretical properties were not
derived. In this paper we use the sieve framework to prove that the estimator
is consistent.
