From theory to practice - page 534
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Thanks for the link, got carried away looking for related ideas. I don't think you need to approach the question as there, from the perspective of R-functions. Approach with conventional means:
Directly from the equation of a circle of radius R with centre coordinates Xc, Yc, ignoring the loss of meaning in units (number, course, distance)
R^2 = (X-Xc)^2 + (Y-Yc)^2
we make a function of the inconsistency at the point with the number i (Xi = i). This is the difference between the distance from point (Xi, Yi) to centre Xc, Yc and radius R:
Di = ((Xi-Xc)^2 + (Yi-Yc)^2)^0.5 - R.
The squares of Di and add up to obtain the target function to be minimized. There are three parameters to be varied: R, Xc, Yc. The outermost (first and last) points have less influence than the intermediate points (no adjacent), I think it is better to multiply the corresponding Di^2 by two. And for your fitting purposes with emphasis on the last points, you can also play with weights of several last points by setting up one more column for weights.
If it is not straight, the units of measurement will have to be taken into account. In order to make X and Y influence almost the same in distance calculation (and R is affected by both), it is necessary to take not i number as X, but the same number multiplied by alignment scale, so that X and Y ranges are close in size.
P.S. It turns out that sernam.ru has very cleverly got rid of accusations of copyright infringement by publishing the texts of books only in parts and without specifying output data, in particular the titles of books. It is possible to find texts on sernam.ru which can be found nowhere else on the internet.
I figured out that I need to minimize using Di = ((Xi-Xc)^2 + (Yi-Yc)^2)^0.5 - R.
Then it will be necessary to plot the found circle by games.
the equation will be.
y=(R^2-(X-Xc)^2)^0.5+Yc
So, don't waste your time with this direction. Although, you may build an indicator based on an arc, rather than a straight line, like the mashka. maybe it will work better than the sma.
this is the formula I took.
the general equation of the arc:
(x - L)^2+ (y + (R - H))^2 = R^2
y = sqrt(R^2 - (x - L)^2) - (R - H) , where the formula for R is in the figure.
But it's only suitable for the positive plane. for the experiment i took an "arc price channel" which lies in the positive plane.
maybe it's just a pretty name chosen...
RRR5:
...
But this is only suitable for the positive plane. for the experiment I took a "price channel on an arc", which lies in the positive plane.
What is a "positive plane"?
What is "positive plane"?
but not this arc.
Well, for an arc like this, it'll work.
but not for this one.
RRR5, you do drawings quickly. With what, I wonder?
I read here about polynomials, ANC, various approximation methods, forecasting capabilities, etc. ...
Some believe in prediction, some do not.
But what I was hoping to find, I never saw.
To try to explain what I mean, I will resort to an analogy with gravity in the universe.
Here's a look at the animated gif I recorded.
Answer the question for yourself. Is it possible to predict the trajectory of each object?
Well, of course you can.
But only if you know information about each object at the moment: its mass, current position and direction of movement, time of its appearance and time of its disappearance.
And then it is a matter of mathematics and calculations, using essentially only one formula (for a variant of classical mechanics for velocities far from the speed of light):
the programme itself is a gravity jammer right here. You can play around with it.
It is also necessary to understand that even our planet does not move in a closed circle, but in fact a three-dimensional sine wave (spiral).
This video demonstrates it clearly:
So what if we don't have information about all the objects?
Can we predict the trajectory knowing only the trajectory itself in the past?
This is where the fun begins.
If someone says that it is not possible, the answer is wrong. An affirmative answer would also be wrong.
The solution to this problem will only be probabilistic.
The problem must be solved from the opposite direction. According to the past trajectory, we must first calculate the probabilistic trajectories of the main "clumps" of objects and their mass. To then predict probabilistic models of possible trajectories.
This is what the basic task of AI is for - pattern recognition.
This, as I understand it, is what Maxim Dmitrievsky was talking about.
About six years ago, I published my first developments in this area in the KB:https://www.mql5.com/ru/code/10882. I just used a polynomial of degree 1 (Linear Regression) for channel recognition there. After that I have advanced considerably in this area. But I don't publish anything and won't for obvious reasons. I only give hints for inquiring minds.
Finding linear channels is essentially finding the centres of these gravitational masses.
There are usually 5-10 such centres (channels) in any instrument (symbol). For the prediction of the price all of them should be taken into account simultaneously. Only in this case the accuracy of prediction going up or down will be much higher than 50%.
But everybody tries to find a special set of numbers and naively believes that they will predict the future.
The matter is that this "set of numbers" alive, dynamic, it constantly changes, as well as position of local centres of masses of set of objects in analogy with a material gravitation changes. And the problem is reduced to finding of the law of change of this "set of numbers" and even finding of the law of change of the law itself :))
Ideally, this "set of numbers" should be recalculated with every tick. This is exactly why I have said more than once that what many call optimisation, finding a particular "set of numbers" is trivial tinkering with historical data.
I think the analogy with gravity is very apt. In the market, gravity is created by money. Some will go in with $100, others with a few billion. The same laws of gravity apply here, and even the same formula I gave above. The force of attraction is inversely proportional to the square of the distance and directly proportional to the masses. Therefore a polynomial regression of degree 2 (parabola) is the most appropriate tool. Although it would be more logical to use a hyperbola, because it is according to the laws of the hyperbola that two gravitational bodies interact. But, the fact is that the parabola is much more convenient for calculations, as well as parabola and hyperbola are very similar to each other at the most important interval.
You can see it clearly here. The red line is the parabola and the blue line is the hyperbola.
The main difference between the gravity of money and the gravity of celestial bodies is that money can suddenly appear and suddenly disappear, creating powerful gravitational fluctuations. But to calculate this event and there is such a thing as a channel breakdown.
The solution to this problem will only be probabilistic.
The problem has to be solved in reverse. From the past trajectory, one must first calculate the probabilistic trajectories of the main "clumps" of objects and their mass. To then predict probabilistic models of possible trajectories.
I'm afraid the "probabilistic solution" here would be the entire set of any trajectories in a given space - and what is the value of that solution ?
That would be like claiming "with high probability" that the Eurodollar will not be negative this year, no more than 100. Notice that the probability of this assertion is close to 100%. But would you get much use out of such a "prediction" ?
In probability theory, it is proved that when the state of an object is influenced by many independent forces, the probability of the state begins to obey Gaussian law. However, the course and value of prices does not obey this distribution, for the simple reason that the inputs and outputs of market participants are dependent.
RRR5:
понял, что минимизировать нужно по формуле Di = ((Xi-Xc)^2 + (Yi-Yc)^2)^0.5 - R.
...
But it is only suitable for the positive plane. For the experiment I took a "price channel on an arc", which lies in the positive plane.
I still don't understand why you don't like the MNC. It's fine to plot any of the above curves.
I like to work on small TFs, but I don't like these snafus.
What can you predict them with?