Let's say I have n time series datasets, each of which displays a very similar pattern—perhaps an essentially flat line with a pronounced bump somewhere in the middle—and I want to display them all in a single averaged plot.
This is all well and good if the bump appears at the same time in each dataset. But what if this bump moves backwards and forwards in time between datasets? In the average time series, the bump will be subject to 'temporal smearing' that obscures the pattern of interest.
Is there any way to average multiple time series in a way that sidesteps this 'temporal smearing' phenomenon and visualises the essential pattern?
EDIT: approaches that communicate the relative certainty/uncertainty in position of hypothetical 'bump' would be especially appreciated. I currently have fixed time-points plotted with vertical error bars, but that's not very effective.