The market is a controlled dynamic system. - page 58
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In kotier it is more complicated - the signal may or may not be present in the mix with the interference!
By suppressing the interference (noise) you can improve the search conditions for the signal, but the problem remains unsolved.
How many signals are there?
How many signals are there?
I wish there were more good ones...)
That's right.
Zero on the input means no signals, no matter how many there are.
You have just substantiated one of the techniques of technical analysis - the construction of trend lines.
Exactly the opposite is true.
Zero on the input is not always zero. If it was not zero a minute ago and the system possesses some memory, the inertial modeling will produce a non-zero output despite the assumption of zero at the input. We will get a deviation from the trend line, and if the model is a bit more complicated than a five penny coin, the picture of the future will be more interesting.
Oleg, it was irony, I forgot to put a smiley at the end of the sentence.)
" here. с #93 ... #96" you directly talk about signal and interference, while in the post I was replying to - not a single word about it.
Apparently, I missed and did not specify that I consider the input stream as an additive mixture of the useful signal and interference:
x(t) = s(t) + n(t)
although I implied it as a matter of course.
Once we have identified the system's parameters, we only have to "let it go" for a short time into the future, so to speak, in inertial mode, and see what happens. In fact, this is the prediction - but only under the assumption that there is nothing at the input of the system at that moment. As it was rightly noted above, we do not know the input signal and can only estimate it using past data, but we have nothing better to predict than to assume that the input is 0.
To be more correct, not input equal to 0, but change in input equal to 0. Although various variations are allowed here, e.g. input change within [a,b]
In kotier it is more complicated - the signal may or may not be present in the mix with the interference!
By suppressing the interference (noise), it is possible to improve the signal search conditions, but the problem remains unsolved.
Quite right.
And we can assume that noise of varying intensities is always present. In contrast to this, the signal at the input may or may not be present (again some tolerances can be introduced). And here we are not far from a clear separation of a trend from a flat.
5) By including an optimisation-adaptation loop, we obtain a closed simulation system
If we describe this scheme from the market point of view, then 2 opposing forces are evaluated from the quote flow using the functions qL and qR - limit orders, which impede the movement and market orders, which create it. They are then compared using q0. Essentially, if the limit side is stronger, we should expect a flat, and if the market side is stronger, we should expect a trend. The adaptation block changes the qL and qR parameters based on the forecast error.
It may be logical to split WL and WR into two blocks. They correspond to liquidity to buy WLb, liquidity to sell WLs, market orders to buy WRb, market orders to sell WRs. WRb interacts with WLs and forms up moves, and WRs with WLb form down moves. The chart will show 4 blocks that interact in pairs and then their results interact with each other via q0. Then in addition to the notion of trending/floating there will also be the direction of movement. I.e. 4 components will be extracted from the quotient instead of 2. Roughly speaking, these are buying forces, selling forces, resistance to buying and resistance to selling.
If we take an analogy from physics) it is as if a body is moving up and down in a dense medium due to impulses applied to it. But the density of the medium changes and it is different in different directions.
The question is these functions qL and qR. Can give as input not only quotients, but also their elementary attributes, which would be hard for them to extract themselves, but which may be decisive in their work. First of all, time attributes (hour of the day, day of the week). Perhaps price attributes such as volatility, reaching extremes.
If you take an analogy from physics), it is as if a body is moving up and down in a dense medium due to the impulses applied to it. But the density of the medium changes and it is different in different directions.
Yes, such an analogy is very clear and useful.
And the problem can be interpreted as the determination of market medium density, density gradient and its change in time.
Similar problems are solved in geolocation (only instead of time there are coordinates of probing signal application) and every day in ultrasound diagnostics rooms.
I) Let's agree to call the instrument a Stock. In general, the laws of behaviour of a stock and a forex pair should be similar.
II) I have divided the market as a whole into two unequal subsystems - the "Stock" proper and "That which is external to it". The interaction between these subsystems is one-way. That is, only "External" influences "Action", but not vice versa. The model describing the motion of the Action corresponds to the "general philosophical" equation of motion from the theory of systems: "The reaction of an object to an impact is proportional to the intensity of the impact and inversely proportional to the inertia of the object". Well, further on, the model is constructed very similarly to how it is described by Landafshitz in his Mechanics. The most important feature of this description is the closure of the difuraa tions relative to changes in the share price, i.e. its main parameter. I.e. we do not use anything besides quotations.
III) Once again: the stock movement diphura was non-linear, i.e. the superposition principle was rejected immediately. It is certain that doubling the external impact on the quote could result in far from doubling the response of the fininstrument. And the presence of memory in the stock sort of hints that the system is fundamentally non-linear (this is not necessarily the case, but we lose nothing here, since non-linearity can always be removed if it becomes superfluous).
IV) There was no attempt to explicitly describe all the possible influences external to the Action. I have bluntly divided them according to the principle of impact on the quote. I got 4 aggregated types:
1) constant impact that is independent of the stock price (Alpha impact),
2) an impact that is proportional to the share price (Beta impact),
3) Proportional to the derivative of the share price (Gamma impact).
4) proportional to the square of the share price (introducing non-linearity) (Delta impact).
It doesn't matter what is inside these types of impacts. The important thing is that we have reduced all of them to four known types, and more importantly, we hope that their parameters can be determined experimentally (so far I only think so).
And then we got this idea of the whole process. All four types of impact are themselves functions of time, and they change relatively slowly relative to the share price. At almost any given point in time, we can assume that these influences do not change and set an equilibrium price for the stock.
Any news changes these influences by leaps and bounds, throwing information into the system that sets a new equilibrium value for the share price. A transient process begins which seeks to align the share price to the new conditions (there it is, OOS in the system!). Roughly speaking, this is a second-order linear diffura. The linearisation of the diphour is obtained by assuming a small magnitude of fluctuations, i.e. deviations from equilibrium values. We get something like a parametric oscillator (i.e. the Action subsystem is an open system!).
Our main task is to determine parameters of these types of impacts as early as possible, and thereby determine how the process itself evolves over time (forecasting). The most important conclusion is this: the share price changes even when external influences are constant (no news). In other words, news does not affect the stock immediately, and the influence of the latest news takes place even a finite time after the news itself.
By the way, linearity of the second-order diffura makes it easy to introduce classical mechanics concepts - the momentum of the stock and the Lagrange function (energy). At the section of invariability of external influences one can speak about some semblance of the energy conservation law as well. In short, it's all out of mechanics. Of course, this is only visibility, since I have made the price of the Stock fundamentally a stochastic process. Under certain, not too restrictive assumptions about this random process it is even possible to derive an equation of this process (which I managed to do - although so far I don't see any use in it).
Guys, if anyone has any signs of strong butthurt about all this scholasticism - ask questions, I'll try to clarify. ATS scheme will be a little later - if you get at least some consensus on the above bullshit.
Those who like to criticise "just because such complex systems can't be reduced to dumb mechanics" please think seriously about the arguments. It's not really "dumb mechanics" at all, just some distant semblance of it. Unjustified criticism will be ignored.
If we describe this scheme from the market point of view, then from the quote flow using the functions qL and qR we estimate 2 opposing forces - limit orders that impede the movement and market orders that create it. They are then compared using q0. Essentially, if the limit side is stronger, we should expect a flat, and if the market side is stronger, we should expect a trend. The adaptation block changes the qL and qR parameters based on the forecast error.
It may be logical to split WL and WR into two blocks. They correspond to liquidity to buy WLb, liquidity to sell WLs, market orders to buy WRb, market orders to sell WRs. WRb interacts with WLs and forms up moves, and WRs with WLb form down moves. The chart will show 4 blocks that interact in pairs and then their results interact with each other via q0. Then in addition to the notion of trending/floating there will also be the direction of movement. I.e. 4 components will be extracted from the quotient instead of 2. Roughly speaking, these are buying forces, selling forces, resistance to buying and resistance to selling.
If we take an analogy from physics) it is as if a body is moving up and down in a dense medium due to impulses applied to it. But the density of the medium changes and it is different in different directions.
The question is these functions qL and qR. Can give as input not only quotients, but also their elementary attributes, which would be hard for them to extract themselves, but which may be decisive in their work. First of all, time attributes (hour of the day, day of the week). Perhaps price attributes such as volatility, reaching extremes.
A very good comparison with the movement of a body in a dense medium under the action of differently directed forces.
As I said before, we then need to solve particular problems, the main ones being:
Having represented the WL and WR blocks as WLs, WLb and WRs, WRb, we can then link them as a cross-over structure.