# Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?

e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is? Also, is the Hurst exponent appropriate for this purpose? The time signals I'm interested in come from natural processes like fluid flow. I want to study signals based on how non-stationary they are.

• I was thinking on a "dynamic index" measure, with 1 a totally dynamical system and 0 a static relationship, or a "periodicity index" measure, with 1 if the signal is periodic or convergent and 0 if is chaotic. For the first case, one would expect the number of estimated states could serve (if such kind of object could be defined). Hence a single index would not be rightly possible?. Maybe the same object for checking chaos-ity indicates how much periodic is the signal. In fact chaos is the contrary of periodic and/of convergent. – Brethlosze Dec 7 '16 at 11:03
• I guess if you may assume stationary for short time then evolution of eigenvlaues over time would reflect nonstationarity. – Creator Dec 7 '16 at 22:40
• For such you need to define order. Which is actually a measure of how dynamic a system is. Not how periodic / chaotic. You should then check the degeneracy of these eigenvalues. If and only if, you have very well identified your system. :) – Brethlosze Dec 8 '16 at 0:58
• yeah, I was thinking along the lines of measuring WSSity by looking how well the Wiener-Khinchin theorem applies e.g. by comparing short-windowed FTs, which is actually just a special case of your eigenvalue considerations. – Marcus Müller Dec 8 '16 at 1:10
• The signals come from flow turbulence, so I can't identify the system too well. What do you folks think about using the Hurst exponent? – atmaere Dec 9 '16 at 5:39