Hearst index - page 24

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What's the problem? I can give you Peters.
 
Toss it over, Alexei. I'll look into it.
 

Here, I've found it. Shit, the file doesn't fit. See the private message.

 
sent
 
I have received the books. First of all, I'll look through them to see if there are any discrepancies in the definitions. In general, I'll get into it for a start ;)
 
avtomat:
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:

2.1. Fractal statistics is unable to distinguish SBs from real markets and mathematically prove their memory effect, and is therefore completely useless.
2.2. Peters is a fraud and is messing with our heads!(unlikely).
2.3. Peters was wrong in his calculations and so was Eric Nyman, who repeated the calculations in his book.

3. I was wrong:

3.1. In the algorithm.
3.2. In methodology.

Would very much like to confirm the third point. I look forward to independent results.

In favour of point 3, says that

1. the curve changes too smoothly. This should not be the case, especially on large averaging periods, as the number of independent RS measurements on large periods is extremely small (1 - 2).

2. Growth is too high. The line reaches almost 2 at the end of the graph, whereas Peters's reaches 1.3. Even with an unvarying slope it's no way more than 1.6, and I have as much as 2! Something's not right here.

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.
 

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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.

 
Did you take the period window as a sliding window? Peters calculates on non-overlapping data (see appendix 3, book one, for his methodology for period layout). But the result should not be very different. Still, the error is obviously somewhere in the layout of the data, but the R/S chart can't have such dips and spikes. It is not clear how you got R/S values below 0.2, when even a very small averaging period N=6 gives 0.28. At the very beginning the graph should be very smooth, because there are so many sub-periods averaged.
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