# Is there a statistic or metric that measures variation (or deviation from mean) in a time-dependent manner?

I am evaluating two time series. One has a larger Coefficient of Variation (CV) than the other. But I have also noticed that one of the time series has longer consecutive deviations from the mean. This is particularly important for the purposes of my analysis. Is there a statistic or algorithm that captures that information? Should I do an ad-hoc metric?

• Perhaps use an error correction model and focus on the coefficient on the error correction term? It shows how quickly a deviation from the mean corrects towards the mean. But that is a bit restrictive; something nonparametric could be nicer. – Richard Hardy Jun 27 '17 at 8:06
• Thank you for the suggestion. in researching error correction, i have come across loss-functions. It looks like i need a loss-function that has memory. – Bobby M Jun 28 '17 at 16:02