Is there a way to test a hypothesis for a time series where $H_0 : \mu <$ threshold ?
For example, if I am monitoring an athlete's heart rate and there is a sudden spike in his heart rate from 100bpm to 200bpm, I want to test if the heart rate's mean is now higher than some average threshold it was previously at.
For example, differentiating between these two series:
100,200,200,150,170,180,170,160,175
100,200,190,120,130,130,140,125,120
Where my null hypothesis would be, following the spike I expect the heart to decrease below 150bpm on average unless given some contradicting evidence. (in reality my series are much longer but this toy example gets the point across).
I know there are mean reversion tests but I am not concerned with a return to some previous mean as I care if the heart rates are below a particular threshold that may or may not be related to the previous mean of the heart rates.
Are there methods aimed at this type of analysis?
