Random Flow Theory and FOREX - page 57
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There is no stationarity! The process is inherently non-stationary. What is a pattern? For example, a Fibo, a Mach, any indicator, etc. Does this pattern bring profit or not? Sometimes it does. In what area is the pattern located? I do not know. Any trading system recognizes some pattern that, in the opinion of the TS author, reasonably or unreasonably possesses some predictive properties. If this TS is built on the assumption of stationarity, then, in my opinion, it will lead to a loss of DEPO, because the market is not stationary. If the TS allows for adaptation (e.g. optimization), then it is closer to non-stationarity. But stationarity as a basic postulate must be forgotten.
The market cannot be non-stationary or non-stationary. There can only be a series of process observations created according to some rule. For example, a sequence of price increments during time t. The task is to find rules for input and output between which the series of prices will be sufficiently stationary. I.e. the system indicators change but slowly enough. Only stationarity, at least temporal, can be traded.
Colleagues, please stop throwing around words whose meaning you do not know exactly, or which are not precisely defined in science, or whose definition clearly contradicts the phenomenon being modelled - price flow.
"Stationarity".
https://ru.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D1%80%D0%BD%D0%BE%D1%81%D1%82%D1%8C
Stationarity is the property of a probabilistic process to remain constant over time.
Let (Ω, F, P) be a probability space and ξ = (ξ1, ξ2, ...) be some sequence of random variables, or a random sequence. Denote by θkξ the sequence (ξk+1, ξk+2, ...). A random sequence ξ is called stationary (in the narrow sense) if for ∀k ≥ 1 the probability distribution of θkξ and ξ is P ((ξ1, ξ2, ...) ∈ B) = P ((ξk+1, ξk+2, ...) ∈ B), B ∈ B(R∞), g de B(R∞) is a Borel σ-algebra.
Stationarity of a random process means that its probability patterns are constant over time, and two kinds of stationarity are usually considered: stationarity in the narrow sense, where the finite-dimensional distributions are invariant with respect to time shifts, and stationarity in the broad sense, where only the mathematical expectations are independent of time. The practical application of stationarity is based on the fact that for a stationary process the characteristics of any random sample and the general population coincide.
That is, our price stream is stationary only on a flat - and on a PARTICULAR flat, with unchanging mathematical expectation. So why would anyone want to model this FLET?
A simple example of stationarity is a coin. If it is correct then the probability of heads and tails is 0.5 each. And each series of tosses will result in a 50/50 split of heads and tails (aim for average). And "the characteristics of any random sample and the general population coincide" will be fulfilled. Even if it is the wrong coin, and it falls with probabilities 0.7/0.3, the series will be stationary (though if we look at the sum of the increments, there will be a trend). A stationary series is one whose estimate of MO for future trials converges to the past estimate and has a finite variance.
Now let's add an option to change coins at arbitrary moments of time. Now let's throw a right coin and then a wrong one, but the observer does not see it, he only sees the sequence of heads and tails. From his point of view, the process will be non-stationary: the estimation of the MO changes involuntarily for him.
A simple example of stationarity is a coin. If it is correct then the probability of heads and tails is 0.5 each. And each series of tosses will result in a 50/50 split of heads and tails (aim for average). And "the characteristics of any random sample and the general population coincide" will be fulfilled. Even if it is the wrong coin, and it falls with probabilities 0.7/0.3, the series will be stationary (though if we look at the sum of the increments, there will be a trend). A stationary series is one whose estimate of MO for future trials converges to the past estimate and has a finite variance.
Now let's add an option to change coins at arbitrary moments of time. Now let's throw a right coin and then a wrong one, but the observer does not see it, he only sees the sequence of heads and tails. From his point of view the process will be non-stationary: the estimation of MF changes involuntarily for him.
That's all well and good. But what does trading have to do with it? What's trading got to do with it? What does trading have to do with flipping a coin? Where is the analogy here?
A market cannot be non-stationary, non-stationary. There can only be a series of process observations created according to some rule. For example, a sequence of price increments over time t. The task is to find rules for input and output between which the price series will be sufficiently stationary. I.e. the system indicators change but slowly enough. Only stationarity, at least temporal, can be traded.
Not this and not that, but which? There is a classification of systems and a fairly large group of people who believe that markets are non-linear dynamic systems. I oppose the following approach. The branch suggests: let us build a mathematical model of BP and, knowing this model, let us make a TS. And they take the simplest model, based on a stationary random process. I think that on the assumption of stationarity of BP it is impossible to create a mathematical model, because BP describes the model in which there will always be uncertain (term) parameters. We should strive for methods that would be able to recognize price patterns that have predictive ability of direction, and ideally the goal of price movement. Neural networks solve such problems, but they are not the only ones.
That's all well and good. But what does trading have to do with it? What's trading got to do with it? What does trading have to do with flipping a coin? Where is the analogy here?
Let's take a series of price movements over time t - returnees. If we investigate this series it will be non-stationary. The task is to find the moments when the series is stationary. In this case, the equity increments will also be stationary. Only when playing the positive stationary MO of the trading system, it is possible to avoid a loss and even profit without relying on luck. Unfortunately abstractions are working in this case :( When trading non-stationary "random values" the loss is just a question of time and the leverage used, even if the IR is zero. Unless of course your capital is significantly less than that of the player you are conditionally playing against.
Oh, read, Chumazik, the discussion on Prival with L-Programmer that I linked to. Read it, don't be lazy. It's not a bunch of suckers. Who are you trying to sell the PTU-schinky understanding of Fourier to here? I'm not going to repeat for everybody here 101+ times why Fourier is erroneous for non-periodic processes and why anybody who is parroting Fourier is just a stupid PTU-shin.
https://forum.mql4.com/ru/19762/page29#174504
" with DFT you get a decomposition of the signal into its components, after which you can NOT say that it is NOT made up of them, ... " - no, it isn't! It's bullshit! It's the biggest bullshit in science in the last 150+ years! You won't get shit! (That's what Lagrange, Laplace and his companions said.) You will get an approximate approximation by the sum of multiples of harmonics, and that sum has to be EACH way - both ways. Where have you seen such a Fourier "spectrum" in real life? Where is there such an infinite spectrum? Where is the computer memory that would accommodate such an infinite spectrum? You see, Prival has got quiet here, probably because he's got some books on FFT and he's realized that it's a real mess here. Take it from him.
By the way, where is he? We're a couple of vocational school kids short of a couple of mathletes with a degree. Where's "Math Math"? We are here humping cool maths for them, while they are all basking in the sand in the Crimea. It's ridiculous!
AlexEro, don't be stupid :) I don't remember all the details, but I didn't mean the full inverse transformation, it's not needed. Do you listen to mp3? Does it bother you that some harmonics are missing there? No? That's true. It's the same principle. But that's not the point. The point is, as I wrote above, THIS WILL NOT work. Because we're interpolating with DFT. Is it clear now?
Not this and not that, but which? There is a classification of systems and a fairly large group of people who believe that markets are non-linear dynamic systems.
I agree, but that term doesn't really do anything.
I oppose the following approach. It is proposed in the thread: let us build a mathematical model of BP and, knowing this model, let us make a TS. And they take the simplest model, based on a stationary random process. I think that on the assumption of stationarity of BP it is impossible to create a mathematical model, because BP describes the model in which there will always be uncertain (term) parameters. We should strive for methods that would be able to recognize price patterns that have predictive ability of direction, and ideally the goal of price movement. Neural networks solve such problems, but they are not the only ones.
A neural network will not give anything without knowing what to send to its input. This is the knowledge about the market, and without it you can learn until you lose heartbeat and fail... NS is a tool, but you have to know how to use it and most often you can do without it. In short, there has to be an idea at the core - an idea of how the market functions. The problem is that we do not know it, as in the example of the nigger - we have never seen them. We only have their footprints and have the opportunity to make assumptions about how they are and what they want. And then to check, to build new ones. And at the end there is a simple system of using the negro's properties))) You could also do the opposite, first stumble upon how one is used and then try to understand the essence of what is used. Again a test to help.
AlexEro, don't be stupid :) I don't remember all the details, but I didn't mean full reverse transformation, it's not necessary. Do you listen to mp3? Does it bother you, that some harmonics are missing there? No? That's true. It's the same principle. But that's not the point. The point is, as I wrote above, THIS WILL NOT work. Because we're interpolating with DFT. Is it clear now?
Ah, pardon, I misspoke again. I applied the term interpolation (mid-interval) as opposed to extrapolation (out-of-interval). Of course I meant approximation. Dear PTU students, don't beat up the nerd...
AlexEro, don't be stupid :) I don't remember all the details, but I didn't mean full reverse transformation, it's not necessary. Do you listen to mp3? Does it bother you, that there are some harmonics missing? No? That's true. It's the same principle. But that's not the point. The point is, as I wrote above, THIS WILL NOT work. Because we're interpolating with DFT. Is it clear now?
I don't listen to MP3s and don't advise others to - because of the implicit hidden spectrum shift, which is very bad for your hearing and generally for your health, I listen to vinyl.