a trading strategy based on Elliott Wave Theory - page 179
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solandr, thank you for your reply.
I've just reread it, I'm surprised myself )))))
I can't remember what I meant to say. ))
I wanted to distract Johnny from his desire to flaunt. ))
i've got to stop watching 10 hours a day )))))
although there is a possibility that some valuable thought was there but got lost in the process of writing the post... ))))
or maybe it wasn't lost.... (I'm sleepy, I'm not thinking straight right now)
We try to predict stable linear regression channels (or trends), and the lifetime of such channels.
Further, we show not yet fully processed data of Hearst index (admittedly, one of its variants) for the sample according to the general rules of its calculation. But certain conclusions can already be drawn. For the long parts (counting from the current 499 bar in the history) we can see a clear tendency to change the "relationship" into the opposite one, not to mention that in the beginning the indicator jumps in the area of - 0.5. For the section around 250 bar, the indicator takes on zero values, which indicates an exact (100%) change in the trend. Starting from 320 counts, there are peaks of Hurst index from 0.8 and up to 1.
The following conclusions can be drawn (based on the sample taken only):
1. The lifetime of long sections (linear trends) is gradually decreasing, and at 250 the trend reverses. This means that the price should turn around.
2. Some strong short parts are formed, in which a new trend (or rather a linear regression channel, whichever is more convenient) is born.
It is possible to check whether the forecast is true. Let's look at the history in the picture. Blue colour stands for the price series used to calculate H, gray color stands for the future. The red color represents the Hearst Index chart.
Judge for yourself, everything is clear... :o)))
In general, rather good results are obtained, for all plots and with different sample lengths. The given example is quite "typical" for my Hurst index, even without using additional criteria.
PS: Maybe someone else could share their results? It would be interesting.
I haven't done any such experiments myself, but I'm sure I'll calculate something similar.
I haven't done any such experiments myself, but I'm sure I'll calculate something similar.
H(k) is the Hurst index. Its going beyond 0 and 1 is not related to the accuracy of calculations. If you look at the formulas, nothing prevents it to be less than zero or more than 1. These data are preliminary, and they still need to be processed (on what I am working).
PS: The only place where "errors" can occur (nothing to do with calculation accuracy or algorithm) is in very small samples.
The 380 count warns of a possible change in the situation, although, as I wrote above, not so much (I have studied the "sensitivity" of the indicator a bit), and is 0.0732
Yes, I understand that on history, you can get smart, but this is research and only part of the system, and old Hirst is slowly revealing his secrets. :о)))
in return, I can offer a quote from a friend of mine... (she works in a memory development centre)
the thing is...
told her what I was doing, what I was studying... this is what she said:
you talk to him for 10 minutes and you start to believe there's something to it, even though you can't figure out what it is.
since then I've defiled the notion of a "numbersetter" as someone delving into a meaningless topic; and clearly articulate the task before researching )))
P.S. (added after 2 weeks... :) )
it turns out they also have a website... http://www.chislonautics.ru/
Very interesting what you have posted. Especially the methodology of calculations and the fact that Hurst goes beyond the interval (0.1).
As to 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, 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.
Maybe for other systems H may be outside this range, but not for bivariate motion.
By the way, at this link http://stocktrade.narod.ru/indicators/FRAMA.pdf
You'll find an article which gives a fairly simple algorithm for calculating D.
I think one can use it to check Hearst "from the other side" :-))
The article may also be of interest to you because it gives a variant of building an adaptive MA.
Of course, one cannot use the data of Hearst Ratio calculation in the form shown in the mentioned posts (it is chaotic and noisy but there are some trends visible to the eye). You must detect the main signal and work with it. As an example, I took an arbitrary sample (it does not coincide with the examples, but it does not matter). The figure below shows the filtered Hearst index signal (red), the sample used for the calculation (blue) and the gray is the fact. Note the structure of the calculated sample (blue), it is not so trivial for prediction.
It is desirable to go through all extrema, but we will limit ourselves to five, the most interesting ones:
----------------------------------------------------------------------------------------------
Extrema Hearst Counting Channel Length
-----------------------------------------------------------------------------------------------
[1]......................51........................0.781..........................549
[2]......................197......................1.113..........................403
[3]......................369......................0.921..........................231
[4]......................441......................0.223..........................159
[5]......................554......................0.701..........................46
Extreme 1
----------------------------------------------------------------------------------------------
Extreme Counting Hurst Channel Length
-----------------------------------------------------------------------------------------------
[1] 51 0.781 549
Most Reliable!!! (I deliberately did not take the whole sample where Hearst is 1.16.) True, the first actual values of this channel go out of range of 1*SCO (and if we take 1.5*SCO, they don't go out at all), but they fluctuate together with the batch, or rather not far and come back to the proper place. It should be noted that of all the variants, this is the longest channel, with more power (not related to sample length), and in general (other criteria for now silent), more adapted to survival.
Extreme 2
----------------------------------------------------------------------------------------------
Extreme Counting Hearst Channel Length
-----------------------------------------------------------------------------------------------
[2] 197 1.113 403
The signal structure element is repeated, and about halfway through the sample the actual data doesn't go anywhere from the channel, which is nothing short of gratifying given the channel length.
Extreme 3
Continues to work. From observations, if any counts are out of 1*SCO on the sample taken as a basis, most likely most (or so) of the actual data will hang around those limits (but these are observations "by eye")
----------------------------------------------------------------------------------------------
Extremum Hearst counts Channel length
-----------------------------------------------------------------------------------------------
[3] 369 0.921 231
Extremum 4
From the Hearst perspective, the structure should definitely change to the opposite. Or rather, there is a very high probability of such an outcome. Which is highly likely to happen, pardon the pun. :о)
----------------------------------------------------------------------------------------------
Extremum Counting Hearst Channel Length
-----------------------------------------------------------------------------------------------
[4] 441 0.223 159
Extremum 5
----------------------------------------------------------------------------------------------
Extremum Counting Hearst Channel Length
-----------------------------------------------------------------------------------------------
[5] 554 0.701 46
(Increased). Changes to the opposite direction and should seem to show 0.0 or so. There are some subtleties related to the short sample length, like 0.7 is not 1.2 at all and somewhere close to 0.6, and where 0.6 is 0.5 :o))) Just kidding. It's just as stable if you take its length into account. Goes on living for a long time, all its original length.
A bit of philosophy
The conclusion about using proper Hearst is quite obvious and confirmed by my numerous experiments (believe me, or I will "flub" with my pictures :o)
Here are some thoughts (I hope, someone will need them):
(1) Each of found channels already has sufficient stability (basically, subsequent data holds within 1-1.5 RMS, and within 2*SCO even more, and keeps its structure) for H values close to 1.0 (or a bit higher). For values close to 0.0 an early reversal of the established structure is confirmed.
(2) The most reliable channel practically always hides behind one of the extremums of R/S signal and therefore additional criteria are required for its identification
(3) Good results are also observed for all values of the price series: Open, High, Low, Close and their arithmetic combinations. And for the calculations I use, as it should be, only one price series (I mean the variant calculated by Vladislav)
(4) When making assumptions about reliability, we should always consider the underlying sample length. A short sample will practically never work for long distances
(5) It is necessary to choose the right structure for its subsequent study (you can of course not choose it). Prediction accuracy is greatly increased by thinking "structurally" about what I want to investigate for robustness. 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
In this example, if you grab more data, the channels found will remain (the current bar is fixed), but there will be new possible variants of long and possibly stable channels.
(6) Interesting topic about channel lifetime prediction.
PS1: So, thanks to Vladislav for his ideas. I was just missing the forecasting part in the system. What's the most surprising, I knew about Hirst for a long time (by my profession indirectly related to diagnostics), but somehow it didn't occur to me to use it, man, what was I thinking ... knowing myself about beer and broads :o)
PS2: Solandr, in general tried for you, knowing how you feel about old Hirst :o)