Figure 1

Jumps are detected by applying a threshold on the increments, but this also creates false positives. Top: An example of a simulated jump-diffusion process where both true jumps (grey dots) and false positives (grey rings) are detected. The inset shows how the jump offset can be registered even if subsequent increments are positive. Bottom: Increment time series of the simulated process in the top panel. A jump is detected every time an increment exceeds the threshold. In this exaggerated case, true jumps are well above threshold, while false positives barely exceed it. This clear separation is not generally the case