Discussion of article "The price movement model and its main provisions (Part 2): Probabilistic price field evolution equation and the occurrence of the observed random walk" - page 9

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Aleksey Nikolayev #:

The problem is that the mean can always be calculated, but it is not always an estimate for the expectation.

The first thing that came up in the search was "sample mean is":


 
Mikhail Tkachev #:

The first thing that came up in the search was "sample average is":


What is the conclusion from what?) You should also give the conditions under which this conclusion is obtained (which variant of the ZBF is used).

At least, the expectation must exist, and this condition does not have to be always fulfilled.

 
Aleksey Nikolayev #:

Conclusion from what?) Please, at the same time, give the conditions under which this conclusion is obtained (which particular variant of the WBC is used).

At least, the expectation must exist, and this condition does not have to be always fulfilled.

I am not that familiar with the subject)
Here is the source : https://sdo.nsuem.ru/mod/resource/view.php?id=74451

 
Mikhail Tkachev #:

I'm not that into it)
Here's the source :
https://sdo.nsuem.ru/pluginfile.php/339455/mod_resource/content/2/Лекция%202%20Мат%20статистика%20.pdf#:~:text=Вывод%3A%20выборочное%20среднее%20является%20точечной,смещенные%20точечные%20оценки%20случайной%20величины

I see. Take, for example, a sample distributed according to Cauchy, for which there is no expectation. Nothing prevents you from calculating the mean for the sample, but it does not converge to anything and does not estimate anything. In such cases, instead of the arithmetic mean of the sample, the matstat uses, for example, the sample median (which is an estimate of the median).

 
Aleksey Nikolayev #:

I see. Take, for example, a sample distributed according to Cauchy, for which there is no expectation. Nothing prevents you from calculating the sample mean, but it does not converge to anything and does not estimate anything. In such cases, in matstat, instead of the arithmetic mean of the sample, for example, the sample median is used.

I can't argue with you, I am a practitioner with average level of abilities)
In samples of increments from price series, the mean is very close to the median, something around 0...
Histograms of such samples have one distinct maximum, similar to normal.
P.S. Now I calculated, the median differs from the mean by 8%, the median is on top, the row of differences of price logarithms.

 
Aleksey Nikolayev #:

There is a rather old book by Peters "Chaos and Order in Capital Markets". In it, if I am not confused, he calculated an attractor for some prices. The dimensionality of the attractor turned out to be quite large, which leads to doubts about the statistical significance of the result (practical usefulness is out of the question).

Yes, I downloaded the book, thanks for the information, I will read it.


 
Dmitry Fedoseev #:

What is it? Is there a new rising star on the horizon, Yusuf 2?

(1) Not just S squared, but modulo S, and only then squared.... What an amazing scientific subtlety.

(2) ...and not a line of code.

(3) The picture is beautiful, and especially impressive for the depth of meaning embedded in it - the orange bar in the upper left corner - you can't argue with that - the probability of price hitting the past is minimal.

So.

  1. Alexei Nikolaev has already introduced you to the simplest properties of complex numbers.
  2. There are 99% of programming articles here without me, we need to diversify the content of the site. And, then, what am I to compete with such "bisoners" as you in this field. I write about what I know.
  3. You have not understood at all what the indicator " Price Probability Distribution" shows. At each historical moment (bar) it shows the probabilities of price values corresponding to it (this moment) in the form of a histogram encoded in a set of colours. It does not show the probabilities of the current price hitting the past (such a thing can only be imagined drunkenly).
 
Aleksey Ivanov #:

Right.

  1. Alexei Nikolaev has already introduced you to the simplest properties of complex numbers.
  2. There are 99% of programming articles here without me, so we need to diversify the content of the site. And, after all, I can't compete with such "bisoners" as you in this field. I write about what I know.
  3. You have not understood at all what the indicator " Price Probability Distribution" shows. At each historical moment (bar) it shows the probabilities of price values corresponding to it (this moment) in the form of a histogram encoded in a set of colours. It does not show the probabilities of the current price hitting the past (this can only be imagined drunkenly).

You have not understood me about the code. Writing formulas that nobody understands is one thing (well, or understandable to 2-3 people, or pretending to understand them).

But to put them in code is to really show that you understand them. Otherwise you get an article about nothing... like 1000 textbooks for universities.

And by the way, I am familiar with complex numbers. So maybe this question of mine is not a reader's problem, but a writer's problem?

 
Dmitry Fedoseev #:

You don't understand me about the code. Writing formulas that nobody understands is one thing (well, or understandable to 2-3 people, or pretending that they understand them).But to put them in code is to really show that you understand them. Otherwise you get an article about nothing.... like 1000 textbooks for universities. And by the way, I know complex numbers. So maybe this question of mine is not a reader's problem, but a writer's problem?

Dmitry, well wait a bit, the author has already done a titanic labour)
I am waiting with interest for some practical conclusions for trading...

 
Inquiring #:


Returning to the graphs, we represent them by an unfolded phase space, superimpose the spirals in the logos (spirit) of the Hopf stratifications, and get the result.

A good programmer is needed.

" A good programmer is needed"...
You have a technical task to develop an indicator/expert/script, for the implementation of which you need a good programmer.
Do I understand you correctly?

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