An apparatus has processing circuitry, and history storage circuitry to store local history records. Each local history record corresponds to a respective subset of instruction addresses and tracks a sequence of observed instruction behaviour observed for successive instances of instructions having addresses in that subset. Pointer storage circuitry to store a shared pointer shared between the local history records. The shared pointer indicates a common storage position reached in each local history record. Prediction circuitry determines predicted instruction behaviour for a given instruction address based on a selected portion of a selected local history record stored in the history storage circuitry. The prediction circuitry selects the selected local history record based on the given instruction address and selects the selected portion based on the shared pointer.