For a multirate sampled-data system consisting of a continuous-time process with or without a time delay, a sampler with period nT and a zero-order hold with period mT (m < n), we study the problem of identifying a fast single-rate model with sampling period mT based on multirate input-output data. This problem is solved in two steps: First, we identify a lifted state-space model for the multirate system by extending existing subspace identification algorithms to take into account the causality constraint in the lifted model. next, based on the lifted model, we extract a state-space model for the fast single-rate system. Such fast-rate models are useful for many applications such as inferential control. Other related topics discussed in the paper include observability of lifted models in the presence of time delay and time-delay estimation from multirate data. Finally, we apply and test the proposed algorithms to an experimental setup involving a continuously stirred tank heater.