This paper investigates performance bounds for joint estimation of signal change point and time delay estimation between two receivers. This problem is formulated as an estimation of the beginning of a well known message and the time shift of its arrival on two receivers from a noisy source. This scenario could be viewed as an extension of the classical time delay estimation [1], [2] with an additional change on the transmitted message. A theoretical derivation of the Barankin bound and a simplified version of this bound are proposed in order to predict the Maximum Likelihood Estimator (MLE) behavior. Simulations illustrate the validity of both bounds but it is pointed out that the MLE seems asymptotically efficient for the normalized time shift estimation contrary to the estimation of message's starting time.