In a recent post you used the words "turning points" that rung a familiar bell to my ears. In a follow-up to that article Dean Teffer complains about the jitter in the signal and the difficulty of defining correctly "turning points", and that also sounds familiar to me.

"Turning points" are typical of studies in materials fatigue. Engineers and statisticians who work in that field have developed "counting methods" (you should like the idea) in order to deal with the phenomenon. Fatigue is a mechanism by which a very small crack in the beginning extracts energy from a load history in order to make its way through a piece of metal. It has similarities with the problems exposed on your site in that the crack is "not interested" in jitter of small amplitude that does not let it open and grow, and in that due to the limitations of the fatigue testing machinery in the labs, the algorithms have to deal with discrete levels.

The most interesting and commonly accepted method for counting in fatigue is Rainflow. Here is a small presentation adapted from a fatigue study. Many results on level-crossing intensities, on time to the next maximum or to the next level-crossing, etc. have been developed by the statistician Igor Rychlik, his mentors Ross Leadbetter and Georg Lindgren, and his group at the University of Lund in Sweden. Even more interesting, all those theoretical results have been practically and reliably implemented into a Matlab toolbox, WAFO.

I have thought for more than a decade that those results might be of interest for trading and finance, but I did not have access to the huge databases necessary to test them in that field, nor the time to go and look for them. Perhaps you can find some bright young student to investigate it. Up to now, we have taken the point of view of the designer fighting fatigue, it would be pleasant to try to play it in the crack's seat!


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