a trading strategy based on Elliott Wave Theory - page 180

 
Hi Yury!
<br / translate="no"> Very interesting what you have posted. Especially the calculation methodology and the fact that Hurst goes beyond the interval (0.1).
Concerning the second point I can share some thoughts. The point is that Hurst is related to D, a measure of fractal dimension, by the formula D=2-H. Or vice versa H=2-D.

The quantity we are measuring, the price, is moving in the (P,T) plane. Its trajectory, depending on its form, can be one-dimensional (a simple smooth curve) or cover part or all of the plane (well, total chaos :-). In the first case, the trajectory dimension is D=1, while in the second case it is D=2. These are obviously extreme variants. In the general case, the trajectory is a random-deterministic price movement, i.e. 1<D<2. Therefore, 0<H<1.


Yes, everything is correct in general, but there is theory and there is practice. As I wrote earlier, professional systems easily produce such results (more than one or less than zero). Parameter processing flattens the result considerably, bringing the data back into that interval.

I didn't have a goal to disprove the foundations, in general what I wanted to tell about is that Hurst is really able to predict by itself, (I hope I've shown clearly, if interested I can take another situation, when there is no trend but a turning point) and does it matter if the value is 1.0 or 1.2? :о)))


By the way, at this link http://stocktrade.narod.ru/indicators/FRAMA.pdf
You'll find an article containing a quite simple algorithm for D calculation.
I think you can use it to check Hearst "from the other side" :-))
And the article may be also interesting for you because it gives a variant of building an adaptive MA.


Thanks, will definitely look into it. :о))

PS: Hope the holiday went well. :о)
 
Made my own version of the indicator - "MQL4: ArrayMinimum() function"
 
I didn't aim to disprove the foundations, in general what I wanted to talk about was that Hurst is indeed able to predict on its own, (I hope I showed clearly, if interested I can take another situation where there is no trend but a tipping point) and does it matter if the value is 1.0 or 1.2? :о)))


Yeah it's not about the hold and the range doesn't really matter. The main thing is to be able to use it.
I only wrote it because we can't calculate the theoretical value in practice. We can only more or less approximate it. This means that the calculation algorithm becomes very important. First of all, it is finite; secondly, it always contains certain parameters that we set with more or less free will. This is most likely where it goes beyond the theoretical range.
For example, the algorithm proposed in the article I cited cannot by definition go beyond theoretical limits. But it has another disadvantage - it has a rather weak range, only about 0.5
 
Rosh
Yes, I did. You made an adaptive MA, and the D calculation there was purely auxiliary.
This D value can also be used completely on its own.
 
<br/ translate="no"> Yes it's not about the establishes and the range doesn't really matter. The important thing is to be able to use it.
I only wrote it because we can't calculate the theoretical value in practice. We can only more or less approximate it. This means that the calculation algorithm becomes very important. First of all, it is finite; secondly, it always contains certain parameters that we set with more or less free will. This is most likely where it goes beyond the theoretical range.


That's right, the main thing is that it should work. And besides it is inherently probabilistic: may be or may not be. As I wrote earlier, it works, at least I have never found on arbitrary samples that none of the proposed channels is completely inappropriate. Practically always the Hurst index finds it. The notion "practically" is used for the case, which I have not encountered for several months of research. In the above calculations, about a third of the channel length, the price is still in the "shadow of the channel", and as this is the H1 period, there is still a day or more to spare. Also, this is only part of the system. :о)))
 
(... I forgot to say earlier :o) When analyzing, you should also look where the current price is relative to the channel. An arbitrary plot on the price series. All symbols are preserved.

The Hurst index


(The same) The noise is removed and the signal is averaged. By the way, in the previous example, smoothing was very strong (all small local extrema were removed). For the current case, it has increased the number of extrema.


Let us consider the minimum. The price is already at the edge of the 1*SCO and taking into account the Hurst score of 0.27 we may be more sure that the price will not return to the channel as we have already seen.


As opposed to the extremum from the previous example where the price is nearly in the centre of the channel:


The main thing, the Arbitrage with a capital letter
Yury, I disagree with you regarding the Hurst indicator. There is no arbitrariness in my understanding of his work. The indicator reveals hidden areas with different persistence, and local extremes "strictly" limit them. Simply put, the indicator says that there are different areas with different structure and these structures can evolve further add: repeating themselves with varying degrees of fidelity and varying degrees of connectivity and impact on the future. Different variations in the development of the situation emerge.

Therefore, my point:
<br/ translate="no"> (5) You need to get the structure right for the subsequent study (you can of course not). Prediction accuracy is greatly increased by thinking "structurally" about what I want to investigate for sustainability. In other words, a channel is a channel (it can be built on any data), but it is important to look at what is in the channel. Sometimes it makes sense to backtrack into history from the current bar


Extremely important!!! Here we can start a long story about fractals and it will be correct, but I will try to make it brief. If you look at the signal taken and the subsequent fact in the current example, of course, the indicator will not display the structure that will form by 1400 bar. It knows nothing about it and will not be able to assess its development. In contrast to the previous example, where the structure just repeated itself and very accurately!!! For the reason that it was already in the sequence, and the situation developed strictly according to it. I.e. we get variants of the situation based on connections, not arbitrary.

Though, the long stretches will show approximate and long position of the price in the channel, if there are at least a few similar structures or directions. Here's just extreme 2:


For that you need to include additional data, i.e. roll back to the future, or rather, to the past, got confused after Alex taught me to plow through time :o). Here's the site under investigation by the way, and if you roll backwards (would know the purchase) the system will show a more accurate direction :o)))):
 
To do that you have to include additional data, i.e. roll back to the future, or rather the past, confused after Alex taught me how to plush the time :o).



I don ' t recall teaching you how to spline time :)))

Actually, the "stretching/shrinking" of time was a quote from Neely.
 
Для этого нужно включать дополнительные данные, т.е. откатываться назад в будущее, вернее, в прошлое, запутался после того, как меня Alex научил плющить время :о).



grasn don't recall me teaching you how to plump up time :)))

Actually, the "stretching/shrinking" of time was a quote from Neely.


I know, it was just a good joke. :о)
 
And to conclude my narrative on the Hearst index, fractality and the issue of "arbitrariness", I think it is interesting to look at the following example of arbitrary sampling at a tipping point. This is an extremely difficult plot, given that a limited sample is taken for the study. The signal under study is marked in red. And it seems to the eye to see that the signal does not include elements of the structure and direction of subsequent data and it seems that RS should definitely be wrong, as the price series will completely change its direction in the future. But let's not be too hasty.


As usual, for reference, the initial Hearst figure


Hearst figure after digital processing. In order not to sound too tedious, I will go straight to the main point. Let's take a closer look at a few local extrema:

----------------------------------------------------------------------------------------------
Extremum...........Counting..........Hurst......................Channel length
-----------------------------------------------------------------------------------------------
[1]...........................287........................0.909..........................413
[2]...........................379........................0.792..........................321


The first local maxima indicate that these channels should exist, for example, extremum [1]. This is what happens, the channel persists for some time


However, there is an extremum [2] which is unremarkable in appearance, but on minimal data it shows what is not visible to the eye, but not noticed by RS statistics. But it is not without an option space. Most interestingly, this count is optimal in terms of accuracy. If you deviate from it in increments of 1 in either direction, the resulting channels will give much worse results.


There are always such channels after calculation, but how to recognize a reliable channel is another story...

That's about it, I guess. Good luck. :о)
 
Very interesting research results! Grasn, thank you for sharing them with the public!