I am trying to measure the variability or "choppiness" of a time series but I am aware that standard measures of standard deviation do not apply due to auto-correlations between the observations.
I am specifically trying to differentiate between series that "flip" sign more than other time series, e.g. consider the two time series
In both, the sum is the same, the average is the same, the max/min are the same, the standard deviation is the same, yet one sequence switches sign only once while the other switches 7 times. Is there a way to measure this? (note I am looking at data this highly non-stationary)
The only idea I can come up with to measure this "choppiness" is to draw a linear line connecting the first number in the series and the last and measure the absolute area between the time series and this straight line. This at least will measure the spread around an ideal path from beginning to end with a smaller choppier series having a smaller value than a larger choppier series, and a perfectly smooth series being close to zero.