a trading strategy based on Elliott Wave Theory - page 306
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The details can be easily reconstructed, especially as the formula uses the fractal dimension and strictly speaking, the equality of the Hurst index to the 2-D value for price series is not observed at all. Dealing with the application of the Hearst figure, I came across this report. The point of my interpretation is to estimate "which way it will go", and there is nothing special in the approach, just simple observations.
If you plot a linear regression on the spread (in general it's not LR at all for the spread) on 221 counts, you can draw the wrong conclusion. Estimating the spread value, and price wandering in the channel, say, according to statistical data, if it happens "soon" (the LR parameters will show it), it should go up, otherwise the price won't make it to the lower boundary (again, if some criteria are met). Let me remind you, at the 221 count we "stand" at the very edge of the channel, and the swing chart doesn't show in which direction the price will "swing". Actually the price will "hang" in the channel for a relatively long time and eventually will move strictly downwards. But using the LR and predicting the spread on its basis is better not to do it, it won't work, though it depends on what it will be used for.
It's clear that the channel spread with a fixed start will be getting wider, but we have to (1) localize the point of expansion and/or (2) estimate the duration of the current channel spread. The first point is a "local trend" and the second point is a "local flat", this is crude, but to put it mildly. By the way, for example, starting from the 600 count, "for some reason, we know that it will be a flat", we could skillfully dispose the deposit (we stand at the border of the channel, we know the statistics of "fluctuations", we know ....). The same situation is for the 221 count, though it is short in duration. And on the 300 count it would be possible to "find" the trend. Similarly, but even more interesting for "price trends", i.e. for LR built on prices (build LR and move to its coordinate system, not forgetting to return back in time).
:о))))
I gave, so to say, some conceptual model from my archive, in general outline, and the formula is not mine, I have deduced mine, but I approached it from the other side.
It's certainly an interesting idea (as the famous satirist used to say). But ...
The Hurst index is essentially an integral characteristic. And prediction is performed (in this case) purely locally. Doesn't that contradict common sense ?
Also, an interesting detail. In both your pictures there is a significant divergence between the red and blue lines. That is the forecast of the swing behavior in the nearest future substantially differs from its actual behavior. How do you manage to get a correct prognosis of the price behavior on the basis of the blue line? :-))
That's right, as forecasting the swing can help a lot. And if one learns to forecast it more or less correctly, in combination with additional series characteristics and processed statistics one can make quite good forecasts for "local trends" and "local flat". In any case, my model certainly has a scope.
The Hearst figure is essentially an integral characteristic. And prediction is performed (in this case) purely locally. Doesn't that contradict common sense?
I need to explain what the term "integral index" means in this context (intuitively I understand it as a stumbling block). And without the term, in terms of common sense, everything is quite normal. At the moment of forecasting we have a series of some length, (in the example "221" and "300") which has some fractal characteristics. Why should it not be used? The formula assumes that the fractal characteristics (or rather, only the fractal dimension, if you look at the formula) will not change significantly for the series in the near future (we should also find out how long it will not). And in general, the shape of this graph correlates with the general shape of the step function of the spread.
Also, an interesting detail. In both your pictures there is a significant divergence between the red and blue lines. That is the forecast of the swing behavior in the nearest future substantially differs from its actual behavior. How do you manage to get a correct prognosis of the price behavior on the basis of the blue line? :-))
And I don't know how to make absolutely accurate predictions of anything for any length. Of course, it makes sense to make local predictions and only at "some points". Besides, you know very well that it is practically impossible to make a forecast for 700 counts ahead over a series of 300 counts. On the graph I made a prediction to the end of the sample. Someone even proved that it is reasonable to make a forecast not more than 1/3 of the initial series length. And consequently it is necessary just to determine for what horizon it makes sense to make a forecast according to this formula. And therefore near to the current "221" and "300" readings this forecast is more or less adequate, approximately for one third of initial sample, roughly speaking. There is no way it will be possible to make absolutely accurate prediction of any length by this formula.
Besides, let's suppose you are at some current readout and then a psychic comes to you and says that the swing graph for 1000 readouts starting from the current one will be like this. Using this chart, can you tell what zones the price will occupy? I think that no, and there are not always moments when you can answer the question: if there is a trend, then in which direction, and if it is flat, then for a long time.
Well, that's good. So it really can be used for forecasting. Good luck.
:о(
Why is it wrong? Up to the 500th count the conclusion is the same - the same process continues. And around the 500th one can already suspect something is wrong. Just relax and find this "hare" in the picture :). The "hare" in this case is a descending channel with false break of the upper border in this very 2nd count
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Couldn't find the hare and the boa calm didn't help. Apparently it's because of their tactical and technical characteristics, they never sit long in one place. What downward channel are you talking about? Then let's put it this way, so that I understand, there is this very 221 count and actually an uptrend channel (if that's what you mean):
There is a swing forecast made by LR and where more or less an approximate future swing value around the 500 count. Still, as far as swing predictions by linear regression are concerned, in this case it's just "lucky". It's rare that the HR will tell you the future swing more or less correctly. Well, ok, being at 221 counts you predicted with the HR that the spread, after almost 300 counts will be about 0.04 and a tails, so it's rough:
So, where is the hare? Can you estimate, using the "221" timeframe, in what direction the channel borders will shift to the "500" timeframe? Will the price move the upper limit or the lower one?
Integral in the sense of calculated for the whole dataset. Since classically Hurst is calculated as an asymptotics of the tangent of the slope, it requires a large enough number of data to compute. So big, in fact, that one can no longer see that the spread changes in a stepwise fashion and, generally speaking, the Hurst definition does not lead to a continuous function.
221 and 300 are not such big numbers. And, furthermore, you are using Hearst in the local sense, i.e. for each channel a different value. If you add at least one sample, you get a different Hearst value. And it's not an indicator, but a function or an indicator. And, of course, it can be used as desired. But this indicator must really "indicate" what you need. :-)
PS
By the way, on your first two pictures of the spread, these
cannot be predicted like that. :-)))
The vertical dotted line marks the current moment and the prediction should only be based on past, relative to the current moment, data. Whether by LR or any other means. So it is totally unclear where the blue dotted line slope in both pictures came from.
I cannot estimate the direction, at least not from the very beginning. And the LR should be corrected as the channel progresses. And by the 300 count the channel will be fine - at least judging from the behavior of the channel spread.
You see, I'm not quite "in the loop" and I am speaking only about what I see in these pictures. Perhaps with a more detailed study I could assert something more specific. But I am engaged now in a little bit other things.