Working within the Nonequilibrium Green's Function formalism, a formula for the two-time current correlation function is derived for the case of transport through a nanojunction in response to an arbitrary time-dependent bias. The one-particle Hamiltonian and the wide band limit approximation are assumed, enabling us to extract all necessary Green's functions and self-energies for the system, extending the analytic work presented previously [Ridley et al. Phys. Rev. B (2015)].