I have a set of time series with events marked in the middle. Following the event there is a temporary dip in the series values followed by a peak so that the area under the curve is 0.
---------|--------\_/'\--------- event response
This response is clearly visible in a plot of the average across all series, but the individual series are too noisy and varied to identify the response visually.
What is the best metric for estimating the statistical significance of this response? That is, how can I be sure it is not just a random artifact?
The event is temporary and short enough to be considered a pulse
This is step-count data in response to the delivery of a brief intervention. Example: subject gets a text message suggesting going for a run.
real data image
Though this effect is not sinusoidal as described above and a bit more exaggerated than the case I'm describing above, here is a plot illustrating a bump response in the averaged signal: