Statistics as a way of looking into the future! - page 16
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Of course, exactly what I asked for.
Just the difference between a chaotic system and a dynamic system is that it is not ordered, i.e. it is not deterministic.
Once again I ask you to point me to the source of the definition, not your interpretation.
Don't waste your time. Linear systems theory is powerless in terms of solving our problems. Linearisation of market processes will only be adequate, if at all, on very small intervals (sub-teak probably), but on those intervals the changes in the system parameter values will be much smaller than the observed noise on the same parameters.
My whole post and this fragment in particular was just a "joke". One thing I learned a long time ago is that what works somewhere and with something will not necessarily work everywhere. (Not having seen the word "any" I also referred to the coryphaeus voiced here :) )
It's just that your argument is already going in circles. And the only criterion of truth can only be "socio-historical practice". ;)
Once again, please point me to the source of the definition and not your interpretation.
I think you will agree that I have had a reasoned conversation with you. So I will now allow myself the impudence and ask you to repay me in the same way: please give me a citation with a link to the source, which states that a chaotic system must be deterministic. For it is already ridiculous, by God.
It's just that your argument is already going in circles. And the only criterion for truth can only be "social-historical practice". ;)
Yes, yes. I'm tired already. Wrapping up.
I think you will agree that I have had a reasoned conversation with you. Therefore I will now allow myself impudence and ask you to repay me in the same way: please give me a quote with a link to the source, which states that the chaotic system must be deterministic. For it is already ridiculous, by God.
About the arguments - I do not agree. The link - Easily.
In the text where we're already talking about "Chaos theory" we read:
>> Chaos theory
Simple nonlinear dynamical systems and even piecewise linear systems can exhibit a completely unpredictable behaviour, which might seem to be random.(Remember that we are speaking of completely deterministic systems!). This seemingly unpredictable behaviour has been called chaos
Any researcher who understands the predictive goals of Dynamical Systems Theory also understands why a system must be deterministic. Otherwise the theory is powerless to assist the researcher in making predictions. What is actually observed everywhere, including in this thread, - no results, but only bragging with names of abstruse mathematical tools, like "stochastic differential equations". Mentioning the regalia of the Nobel Prize winner next to the name of a mathematical tool does not seem to me to confirm the relevance of using the Dynamic Systems Theory in the price forecasting. I suppose that I won't get a sensible explanation why the price spread on the bread of the dynamic systems theory is an edible sandwich, may be the answer of the following kind: because it's spread, it must be edible, or the system is systematic, and equations are stochastic, or everything fits with Kepler, and another got the Nobel Prize... Anyway, I can do this kind of exercise on my own, without any help from anyone else. I'm sorry too.
Now, let's get into the concept switch. The piece of wikipedia you quoted talks about seemingly unpredictable behaviour of deterministic dynamical systems. This partly overlaps with my explanations of how real chaotic systems can be modeled by dynamical ones. However, it is completely unacceptable to confuse the concept of a chaotic system and a dynamical system with chaotic behaviour. They are two completely different things.
So you have not given me the definition of a chaotic system as I asked you to do. I have had plenty of time to appreciate your knowledge in this area as well as your approach to this discussion. I have no interest in discussing this topic with you further.
To prevent further accusations in the spirit of those already outlined, here is the real definition of a chaotic system:
"Chaotic is a system whose state depends randomly on time and initial state." - V.S. Anischenko, T.E. Vadivasova, V.V. Astakhov, V.V. Nonlinear dynamics of chaotic and stochastic systems. Fundamental Fundamentals and Selected Problems. 1999
Now, let's get into the concept switch. The piece of wikipedia you quoted talks about seemingly unpredictable behaviour of deterministic dynamical systems. This partly overlaps with my explanations of how real chaotic systems can be modeled by dynamical ones. However, it is completely unacceptable to confuse the concept of a chaotic system and a dynamical system with chaotic behaviour. They are two completely different things.
So you have not given me the definition of a chaotic system as I asked you to do. I have had plenty of time to appreciate your knowledge in this area, and your approach to this discussion. I have no interest in discussing this topic with you further.
To prevent further accusations in the spirit of those already outlined, here is the real definition of a chaotic system:
"Chaotic is a system whose state is randomly dependent on time and initial state."- V.S. Anischenko, T.E. Vadivasova, V.V. Astakhov. Nonlinear dynamics of chaotic and stochastic systems. Fundamental Fundamentals and Selected Problems. 1999
Quite right, only according to this definition of a chaotic system, a dynamical system cannot be a mathematical model for this chaotic system, since the state of the dynamical system is uniquely determined by time and initial state. In other words, there is no such thing as a chaotic dynamical system.
To understand this you have to multiply two by two, namely to take and study not only the definition of a chaotic system, but also a dynamical system. I purposely gave you an example of a chaotic system from "a piece of wikipedia about dynamical systems" to make it clear that 2x2=4. That only those(deterministic!) chaotic systems that fit into the framework of Dynamical Systems Theory can be predicted. The other definitions of chaotic systems are approached in the same way - we check whether the chaotic system in question is relevant to any theory, including dynamical systems. This is a very simple job that anyone should do. Try to fit your definition into Dynamical Systems Theory before you attack the personality rather than the arguments of your interlocutor.
Do you have an explanation as to why the price or chaotic system in your definition fits within Dynamic Systems Theory?