In this paper, the problem of identification of time-varying systems is investigated in the framework of worst-case identification and information-based complexity, Measures of intrinsic errors, termed persistent identification errors, in such identification problems are introduced, For a selected model space of dimension n (finite impulse response models) and an observation window of length m, the persistent identification measures provide the worst case posterior identification errors over all possible starting times of the observation windows when the input and identification algorithms are optimized, For linear time-invariant (LTI) plants with unmodeled dynamics belonging to certain types of prior unstructured uncertainty sets, upper and lower bounds of the persistent identification measures are explicitly computed, It is shown that when prior unmodeled dynamics are balls in the l(1) space, the lower and upper bounds coincide, In this case, any full-rank periodic probing signals are optimal, and the standard least-squares estimation is in fact an optimal identification algorithm. Motivated by closed-loop identification problems, the concept of nearly periodic signals is introduced, It is shown that such signals are asymptotically optimal for persistent identification and at the same time can be generated in a closed-loop configuration, For slowly varying systems, the persistent identification measures are shown to be continuous functions of the plant variation rates. Furthermore, periodic signals are asymptotically optimal in the sense that they achieve identification errors which approach the optimal persistent identification errors for LTI systems when the variation rates of the plants become small. This result verifies that the persistent identification measures are indeed benchmark values for the identification of time-varying systems.