Two-particle correlations in pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV are studied as a function of the pseudorapidity separation (△η) of the particle pair at small relative azimuthal angle (|△ϕ| < π/3). The correlations are decomposed into a jet component that dominates the short-range correlations (|△η| < 1), and a component that persists at large △η and may originate from collective behavior of the produced system. The events are classified in terms of the multiplicity of the produced particles. Finite azimuthal anisotropies are observed in high-multiplicity events. The second and third Fourier components of the particle-pair azimuthal correlations, V_2 and V_3, are extracted after subtraction of the jet component. The single-particle anisotropy parameters v_2 and v_3 are normalized by their laboratory frame midrapidity value and are studied as a function of η_c.m.. The normalized v_2 distribution is found to be asymmetric about η_c.m. = 0, with smaller values observed at forward pseudorapidity, corresponding to the direction of the proton beam, while no significant pseudorapidity dependence is observed for the normalized v_3 distribution within the statistical uncertainties
