# Measuring how “changey” a time series is over time

I am currently working with a medical dataset which among other things contains data on usage of certain instruments as well as power levels. I am attempting to monitor how "fidgety" a care provider is with a given instrument by calculating some statistic which scores how often the power level is changed. This is somewhat of a vague request because I do not have the vocabulary to describe exactly what I need, but I will attempt to give some examples. This statistic would measure very low if over 15 minutes the instrument was off for 5, on an arbitrary power for 3 minutes, and then off for the rest of the period. It would be higher if instead of being at one power level, it fluctuated, or if it was turned on and off multiple times. I was thinking the answer may be to sum a moving standard deviation, but I am not sure how to normalize this so that it is a meaningful value over slightly different encounter lengths.

• Not that this question seems to involve statistics per se, but since your goal is to measure "how often the power level is changed", why not literally use that? If it doesn't capture everything you need, you could make it one part of a scale that is also made up of some other indicator(s). – rolando2 Jul 30 '18 at 21:03
• The signal I have is the actual speed and it fluctuates with use i.e. 40000 rpm might read as 39908 or 40432, so counting literally how often it changes would drastically over count the jitter. I want something that will notice on/off or about 40000 rpm -> about 10000 rpm and back over small variations – Henry Prickett-Morgan Jul 30 '18 at 22:11
• I'm curious whether you ever found a best course of action on this. – rolando2 Aug 10 at 11:13