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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.

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An increasingly common way to show uncertainly is with spaghetti plots (Andrew Gelman blog posts), which use overlaid translucent lines. The plot gives a raw view without assuming any model. That may be an advantage in this case since more uncertainty indicators assume all the uncertainty is in the Y direction, but you want to given a sense of the pulse location uncertainty instead.

20 overlaid lines:

enter image description here

Another approach is to use uncertainly bands, which is equivalent to your error bars, but maybe neater.

Same data showing quartiles:

enter image description here

Either of these plots could be combined with a plot showing just the uncertainty of the pulse location:

enter image description here

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  • $\begingroup$ Thanks! I had experimented with spaghetti plots, but they were a bit messy. The uncertainty bands are very clean and effective. $\endgroup$
    – Roger
    Nov 18 '14 at 7:30

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