In a holographic description of inflation, cosmological time evolution in the bulk is expected to correspond to the renomalization group (RG) flow in a dual boundary theory. Here, we analyze this expectation by computing the correlation functions of the curvature perturbation holographically. In standard single field models of inflation, the curvature perturbation is known to be conserved at large scales under very general conditions. However, we find that this is not generically the case in the dual description. We discuss the implications of this study on (A)dS/CFT. We also discuss the expected impacts on the observational cosmology.