[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 389

 
FreeLance: Galton's carnations are closer to me.

Yes, quite a visual thing, just looked it up.

joo: sort of ==

What an interesting analogy...

Farnsworth: And where does the process begin? Does it start all the time or does it end all the time? Or does it never stop? That's the answer and the salt. :о)

Well yes, that seems to be how SB is studied: they fix the beginning of a process in the past and look at trajectory characteristics starting from that point. But how to find this point in the real world, has anyone thought about it? Surely, there are such points in the Finns. They are all made of heterogeneous pieces of SB.

 
Mathemat:

Yeah, it's quite a visual thing, I've just had a look at it.


if hammered in dead - one cortina.

But if you introduce "some flimsiness" to the nails...

It's a curious picture. A thick-tailed rossi of pellets.

;)

 

Allow me to insert my nickel. It's calledthe Hearst exponent, but what does it actually indicate? According to the Wehrstrass approximation theorem, any time series on a span can be approximated by polynomials. And then there's the Fourier decomposition and a lot more. In general, any sequence of numbers may turn out to be an absolutely non-random sequence and it is difficult (or impossible?) to distinguish it from a random one by its form. On the other hand, even fragments of random length that coincide even with well-known non-random sequences (like periodic functions) can be found in a perfectly random time series. You can also perform experiments - calculate the exponent for example for a sequence taken from Pi (and you can check, it will not be constant during the time series). So what does Hurst point us to?

 

to FreeLance

учёными мужами не пререкаются...

no way! Optimising costs, I sculpted the Peters bust myself and had a secret cult of it.

Galton's carnations are closer to me.

Everyone broadens his or her mind in his or her own way ...

to Mathemat

Well yes, SB seems to be studied this way: they fix the beginning of the process in the past and look at the characteristics of the trajectory starting from this point. And has anyone ever thought how to find this point in reality? Surely there are such points in the Finns. They're all made of different pieces of SB.

"I am building my strategy around that, only a bit more complicated. By the way, do you remember this thread: https://www.mql5.com/ru/forum/122622 You as a person close to you - ask a question, for sure they will answer it. They didn't even pay attention to us then :o(.

to NorthAlec

Let me insert my nickel. It's called "Hearst's exponent" but what does it actually indicate? According to Weierstrass approximation theorem, any time series on the interval can be approximated by polynomials. And then there's the Fourier decomposition and a lot more. In general, any sequence of numbers may turn out to be an absolutely non-random sequence and it is difficult (or impossible?) to distinguish it from a random one by its form. On the other hand, even fragments of random length that coincide even with well-known non-random sequences (like periodic functions) can be found in a perfectly random time series. You can also perform experiments - calculate the exponent for example for a sequence taken from Pi (and you can check, it will not be constant during the time series). So what is Hurst pointing at?

Do you want to talk about it? 6o)(just in case - kind of a joke)

 

Farnsworth

you have too much respect for him (Hearst). Or is it just me? To me, this whole fractal theory thing has nothing but pretty eyes... And I don't like it just for its pretty eyes.

 
NorthAlec:

Farnsworth

you have too much respect for him (Hearst). Or is it just me? To me, this whole fractal theory thing has nothing but pretty eyes... And I don't like it just for its pretty eyes.

And you read more, it will not seem, some pages ago wrote:

Only, why do you need this indicator? It has a very vague prognostic property (). I.e., even a calculated exact value of 0.8 (even with a confidence interval) - will not tell you anything about the "trendiness" to persist, ...o for his

on this page:

Forex is a process, to put it mildly, weakly self-similar and does not obey a degree dependence.

But that is not the point. fractal analysis is not just a picture of a fern, it is a very complex theory, packed with mathematics, and it is a very young and unformed theory. And it is one of the key and few ways to understand the market.

So - I respect both the analysis and respect old man Hirst, at least for his humble genius.

 
Farnsworth:

... A very complicated theory, packed with maths ...

Sergey, could you give some links for example to see this mathematics.

I also like fractal analysis, but so far I thought, and still think, that there is very little mathematics there and it's too simple.

 
Mathemat:

Yes, that seems to be how SB studies it: they fix the beginning of the process in the past and look at the characteristics of the trajectory starting from that point. Has anyone thought about how to find this point in the real world? Surely, there are such points in the Finns. They are all made of heterogeneous pieces of SB.


Well, most of TC deals with it: they define whether it is a trend or a flat. The other part of TS defines what prices are cheap for this trend or flat, and what prices are expensive to buy cheap and sell expensive. And then there is the cancellation of the scenario. That is why there are a lot of ways of marking this point or window where the necessary process is developing. But you can probably divide it into two classes: fixed window size and adaptive.
 
Yurixx:

Sergey, could you give me a couple of links to see this mathematics as an example.

I like fractal analysis too, but so far I thought and still think there's very little mathematics there and it's too simple.


I forgot to add "difficult for me" :o). Good books are slowly beginning to appear. I don't have all of them in electronic form, but the titles and some books are attached:

  • A. Potapov "Fractals in Radiophysics and Radiolocation. Topology of Sampling". This book is fundamental, I am sure you will like it, especially as you are a physicist. 800 p., of which half is a rigorous (as much as possible) exposition of theory and applications.
  • OI Shelukhin, A.V. Osin, and S.M. Smolsky, "Self-similarity and Fractals. Telecommunication Applications", 400 pp.
  • A.A. Lyubushin, "Analysis of data of geophysical and ecological monitoring systems," Multifractal analysis section.
  • Gregory Wornell "Signal processing with fractal: a wavelet based approach", a very good book, you should be familiar with it.
  • D. Harte "Multifractals.Theory ans applications" in the attachment,
  • M.I. Kulak "Fractal Mechanics of Materials", not yet read, see in the attachment
  • Cronover R.M. "Fractals and Chaos in Dynamical Systems". Fundamentals of Theory" - well systematized material, as a reflection. See attachment
 
Cronover R.M. Fractals and chaos in dynamical systems. Fundamentals of theory
Reason: