Rescaled Range and "Persistence"

[Jimster41]

Why is "black noise" 1/(f^B) where B>2 associated with "persistence" and "long range dependence"?
This book I'm reading uses the level of the Nile river as an example... I can understand what the Rescaled Range is saying but i don't get the implications w/respect to those terms or phrases. Is the idea that there is some relaxation process or processes with very long relaxation times? If so doesn't that somehow suggest one Nile flood is connected to another Nile flood by that process? This seems absurd, what process?

 

[haruspex]

Why is "black noise" 1/(f^B) where B>2 associated with "persistence" and "long range dependence"?
This book I'm reading uses the level of the Nile river as an example... I can understand what the Rescaled Range is saying but i don't get the implications w/respect to those terms or phrases. Is the idea that there is some relaxation process or processes with very long relaxation times? If so doesn't that somehow suggest one Nile flood is connected to another Nile flood by that process? This seems absurd, what process?

I can imagine two such processes. Maybe it relates back to similar persistence in rainfall, perhaps connected with the Southern Oscillation Index. Or low rainfall at the source catchment in one season may leave to its being relatively dry at the start of the next wet season, so more water is retained locally and less floods down.

 

[Jimster41]

Thanks, I sort of came to the same conclusion (that there is some causal geophysical system at work over that time scale) last night while trying to figure out why this example of noise, chaos, fractals has me hung up when the dozens of others the author has described have been easier to grok (book is the one by M. Schroeder: "Fractals, Chaos, Power Laws...")

The part that I'm confused about is how you can have a function (the "rescaled range") of delta t (time interval) and still have something that is noise, which I was thinking had to be random in time. In other words (let me phrase this carefully) why doesn't R(deltat), because it is detectably a function of time, imply regular, structured, periodic, wave-like in space-time? Or is it one of those but not all?