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Here, I've found it. Shit, the file doesn't fit. See the private message.
I have received the books. First of all, I'll look through them to see if there are any discrepancies in the definitions. Anyway, I'll get into it for a start ;)
Thanks for your interest.
Translated the calculation into C#. The algorithm has fully mimicked the Peters methodology. The graph is shown below.
Original
Well, what can I say. The results are much more like those from the book. The line itself has also become similar to the real one. It has a positive slope throughout the entire period (coincidence with the theory), it is smoother at the beginning and becomes more broken at the end (coincidence). However, it is depressing that the slope coefficient does not change (it is actually the Hurst coefficient).
This could mean the following:
1. the process under study has an infinite memory. But the memory must be finite because we are studying a real SP 500 market.
2. the process under study is indistinguishable from a random walk (perhaps it is). Then the Hurst coefficient must be equal to 0.5 for the whole curve interval. If this is indeed the case, then:
3. I was wrong:
Would very much like to confirm the third point. I look forward to independent results.
In favour of point 3, says that
Z.I. A preliminary estimate of the RS slope tangent gives values of about 46% (1.6 time to 1.66 swing), which means there is no trendiness or anti-trendiness and is an obligatory feature of SB.
Having analysed the results, I realised that the mistake may still lie in the fact that Peters didn't mention anything for a reason about restoring returns to the accumulative chart . Eureka!!! He doesn't accumulate anything, but works with an independent series of increments like ln(Pi / Pi-1). My series, on the other hand, was a sum of returns: S += ln(Pi/Pi-1). Then I changed the code and just skipped this operation. The results have dramatically improved:
The results of the average graph began to converge fundamentally with Peters' calculations. True, there are some inaccuracies in the minutiae, in particular there is still a difference between the maximum and minimum levels. Also the local bends of the straight lines are different, but the main points are shown accurately. It can be seen that after a certain time exceeding about 1.9, the angle of inclination has decreased.
What seems interesting is that the accumulative plot of returns (first from the left) follows exactly the random walk. So far I cannot give an explanation for this effect. Logically the picture should not change fundamentally depending on whether we take the returns or their accumulative series, but it is perfectly clear that this is not the case. But why?
A very interesting picture seems to begin to emerge!
p.s. Apparently there are some non-principled differences between Peters and me in the data processing, so the graphs are not much different after all..
So far I've got it that way. But there's something I don't like here. I marked the corresponding points, but I need to cut off the excess -- the data in the original picture are limited to values about log(k)=0.8 and log(k)=2.4
I'll look into it further.