Using a first-principles approach, we calculate electronic and optical properties of molecular aggregates of the dye amphi-pseudoisocyanine, whose structures we obtained from molecular dynamics (MD) simulations of the self-aggregation process. Using quantum chemistry methods, we translate the structural information into an effective time-dependent Frenkel exciton Hamiltonian for the dominant optical transitions in the aggregate. This Hamiltonian is used to calculate the absorption spectrum. Detailed analysis of the dynamic fluctuations in the molecular transition energies and intermolecular excitation transfer interactions in this Hamiltonian allows us to elucidate the origin of the relevant time scales; short time scales, on the order of up to a few hundreds of femtoseconds, result from internal motions of the dye molecules, while the longer (a few picosecond) time scales we ascribe to environmental motions. The absorption spectra of the aggregate structures obtained from MD feature a blue-shifted peak compared to that of the monomer; thus, our aggregates can be classified as H-aggregates, although considerable oscillator strength is carried by states along the entire exciton band. Comparison to the experimental absorption spectrum of amphi-PIC aggregates shows that the simulated line shape is too wide, pointing to too much disorder in the internal structure of the simulated aggregates.