The market is a controlled dynamic system. - page 341
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This does not change the essence of the case.
Before a meaningful conversation about the substance of the case can begin, it must be ensured that everyone involved is speaking the same language and talking about the same things. Therefore, it is common to use language and concepts that are more or less well-established in the field under discussion.
First, some demonstration pictures of comparative behaviour.
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Recall that the true nature of the non-stationarity is not known a priori.
But the estimation of the non-stationarity model can be done by adaptive filtering methods.
szy
I made the pictures in this way for more clarity.
"And I gave my heart to the knowledge of wisdom, and to the knowledge of folly and foolishness: I learned that these also are languor of the spirit: for in much wisdom is much sorrow; and he who multiplies knowledge multiplies sorrow.
Solomon. Bible.
Are you recommending a return to the Stone Age? Or, "none of your business"?
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Of course. Pithecanthropes belong there!
Before starting a meaningful conversation about the substance of the case, it is important to make sure that everyone involved is speaking the same language and talking about the same things. This is why language and concepts that are more or less established in the field under discussion are usually used for this purpose.
I think it is clear from the pictures what we are talking about.
It is not the form of description that is important, but the differences in behaviour. In order to have a meaningful conversation about the essence of the matter, it is necessary to understand these differences.
another picture, useful for understanding the phenomenon:
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I pay special attention to the fact that here the "additive non-stationarity" has as parameters (amplitude, frequency, phase) deterministic smooth time functions. There are no stochastic inclusions. And what is the result ;))
and a couple of other helpful pictures to help you understand
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and a couple of other helpful pictures to understand.
The pictures are beautiful, no doubt about it. I will also give examples of pictures, but later. For now, I will conclude my discussion of the differences in the mathematical understanding of the "stationary process" by the example of your equation dx/dt=Ax:
1) This notion does not refer to the differential equation itself, but to its solutions: x=x(t). This is an important distinction because the same x(t) can be specified in an infinite number of ways (not just by this equation).
2) The solutions to the equation are deterministic, so they will be degenerate random processes which will only be stationary being the identical constants x=x(t)=const. If A is not identically zero, then only the solution x=0 will be such.
As you see, this is an entirely different concept.
But all this is a formality not very interesting for traders, so later I will post pictures showing the advantages of the stochastic approach even in the case of dynamic systems.
The pictures are beautiful, no doubt about it. I will also give examples of pictures, but later. For now, I will conclude my discussion of the differences in the mathematical understanding of the "stationary process" on the example of your equation dx/dt=Ax:
1) This notion does not refer to the differential equation itself, but to its solutions: x=x(t). This is an important distinction because the same x(t) can be specified in an infinite number of ways (not just by this equation).
2) The solutions to the equation are deterministic, so they will be degenerate random processes which will only be stationary being the identical constants x=x(t)=const. If A is not identically zero, then only the solution x=0 will be such.
As you see, this is an entirely different concept.
But all this is a formality not very interesting for traders, that is why I will post later some illustrations showing the advantages of stochastic approach even in the case of dynamic systems.
Here a simple one-dimensional process is considered as an illustrative example. For processes with a dimension greater than two, everything is much more complicated.
A prime example is the Lorenz attractor--there is no determinism in its solutions.
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The object of our interest (and research as much as possible) are time series of quotes that may be considered as solutions of evolution equations (infinite dimensional). There are deterministic (main) and random components in them. However, the character of movement (appearing random) is determined by the structure of the system of evolution equations, but not by the random component.
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The video shows the effect of changes in parameters on the nature of the phase trajectory motion.
don't see any discussion, does anyone even understand what the ***341 page is? It's been seven years.
"Do you see a gopher? - No. But he does." (С)