The transient quantum statistical properties of the atoms and molecules in an atom–molecule BEC system are investigated by obtaining a third-order perturbative solution of the Heisenberg’s equations of motion corresponding to the Hamiltonian of the system, where two atoms can collide to form a molecule. Time dependent quantities, like two boson correlation, entanglement, squeezing, antibunching, etc., are computed, and their properties are compared. It is established that the atom–molecule BEC system is highly nonclassical as lower-order and higher-order squeezing and antibunching in pure (atomic and molecular) modes, squeezing and antibunching in compound mode, and lower-order and higher-order entanglement in compound mode can be observed in the atom–molecule BEC system. Exact numerical results are also reported and the analytic results obtained using the perturbative technique are shown to agree with the exact numerical results.