  Parameters of differential equations are essential to characterize intrinsic
behaviors of dynamic systems. Numerous methods for estimating parameters in
dynamic systems are computationally and/or statistically inadequate, especially
for complex systems with general-order differential operators, such as motion
dynamics. This article presents Green's matching, a computationally tractable
and statistically efficient two-step method, which only needs to approximate
trajectories in dynamic systems but not their derivatives due to the inverse of
differential operators by Green's function. This yields a statistically optimal
guarantee for parameter estimation in general-order equations, a feature not
shared by existing methods, and provides an efficient framework for broad
statistical inferences in complex dynamic systems.
