I have measured a lot of daily activity of people, with data for one person looking like in this image:
I would now like to automatically estimate the time when this person wakes up, and more generally, extract one coherent interval from (in this image) around 5:00am to 10:00pm as the "active" interval, i.e. where this person is awake.
The following line is the per-time-point standard deviation for one person, which shows the clearest separation from day and night so far.
I have brainstormed a few ideas, like tree stumps, something similar to HPD intervals, Hidden Markov Models, or k-means of the y values. But none would result in exactly one coherent interval of higher activity.
What methods would you suggest to split the day up into two intervals using this data?
I'm not even sure if it's better to work with the set of raw days, or the single line of standard deviations (the means have a similar shape but are not so well separated).