Matstat Econometrics Matan - page 30
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Well, for a sine wave is possible, for example)
Not necessarily) If the frequency, amplitude or initial phase is not known with absolute precision, there will be an error. In the case of an inaccurate frequency, the error can become as close to the maximum possible)
I suggest another prediction example - the number three will always be three)
Not necessarily) If the frequency, amplitude or initial phase is not known with absolute precision, there will be an error. In the case of an inaccurate frequency, the error can become as close to the maximum possible)
I suggest another example of a prediction - the number three will always be three)
the "hanging in the air" option is unrealistic in our universe)
In the financial markets, this option is used quite well - before the event, the outcome is already known to a certain group of people - an insider
Alexey! I saw a contradiction in your words: https://www.mql5.com/ru/forum/375685/page9#comment_24113305: " Randomness in the theorem is not defined as a concept at all, but is simply used as a part of terms. Therefore, reasoning about randomness as a certain specific concept is usually inherent to people who are unfamiliar with theorists and matstata.
How should the book "M. Kendel. Time series M.:Finance and Statistics, 1981.-199s." (attached), where one of the 12 chapters is called: "Criteria of Randomness"? When probability theory is stated, combinatorics (number of combinations, permutations, etc.) turns out to be the basis for deriving terver formulas, doesn't it? Randomly pulling socks of two colours out of a drawer in the dark, remember? It is the notion of randomness that leads to the "Number of turning points" criterion, which should be about 2/3 of n in a time series of n points. There are at least a dozen such criteria in the book.
Why not consider the notion of randomness quite definite at least on the basis of even this one book? Its author can by no means be considered uninformed, only a few of his monographs have been translated into Russian:
Wiki:Kendall,_Maurice_George.
PS. By the way, by the number of pivot points criterion, it immediately comes out that forex quotation series (not 2/3 n, but noticeably rarer) are far from random. In other words, they have a memory, they are trending (not counter-trending).
Alexey! I saw a contradiction in your words: https://www.mql5.com/ru/forum/375685/page9#comment_24113305: " Randomness in the theorem is not defined as a concept at all, but is simply used as a part of terms. Therefore, reasoning about randomness as a certain specific concept is usually inherent to people who are unfamiliar with theorists and matstata.
How should the book "M. Kendel. Time series M.:Finance and Statistics, 1981.-199s." (attached), where one of the 12 chapters is called: "Criteria of Randomness"? When probability theory is stated, combinatorics (number of combinations, permutations, etc.) turns out to be the basis for deriving terver formulas, doesn't it? Randomly pulling socks of two colours out of a drawer in the dark, remember? It is the notion of randomness that leads to the "Number of turning points" criterion, which should be about 2/3 of n in a time series of n points. There are at least a dozen such criteria in the book.
Why not consider the notion of randomness quite definite at least on the basis of even this one book? Its author can by no means be considered uninformed, only a few of his monographs have been translated into Russian:
Wiki:Kendall,_Maurice_George.
PS. By the way, by the number of pivot points criterion, it immediately comes out that forex quotation series (not 2/3 n, but noticeably rarer) are far from random. In other words, they have a memory, they are trending (not counter-trending).
No, no and no) The theorem is based on Kolmogorov's axiomatics. Socks and dice and coins etc are just ways of setting up specific probability spaces. Also, historically, they are the forerunner of the modern theorver.
Kolmogorov's axiomatics starts with notions like "random event", but this is just a well-established name for some sets. Like "guinea pig" is an established name for some rodents.
The kind of randomness you're talking about is a term that (usually) means a sequence of independent, equally distributed random variables. This is, for example, what the GCG should produce, and random walk increments, and white noise, etc. etc. (in the scientific literature the abbreviation i.i.d. is often used). As you can see, the basic concept here is "random variable". This, in turn, is just a well-established name for some functions mapping a probability space to a number line.
There is a famous joke among mathematicians - "there is nothing random about random variables")
No, no and no) The theorem is based on Kolmogorov's axiomatics. Socks, dice and coins etc. are just ways of setting specific probability spaces. Also, historically, they are the forerunner of the modern theorver.
Kolmogorov's axiomatics starts with notions like "random event", but this is just a well-established name for some sets. Like "guinea pig" is an established name for some rodents.
The kind of randomness you're talking about is a term that (usually) means a sequence of independent, equally distributed random variables. This is, for example, what the GCG should produce, and random walk increments, and white noise, etc. etc. (in the scientific literature the abbreviation i.i.d. is often used). As you can see, the basic concept here is "random variable". This, in turn, is just a well-established name for some functions mapping a probability space to a number line.
There is a famous joke among mathematicians - "there is nothing random about random variables")
No, there isn't and there isn't.
There is a clear definition of a deterministic, random and stochastic quantity.
"A well-known joke among mathematicians" means that all quantities for which there is no known function that determines their values with 100% accuracy are random or stochastic. This does not mean that such a function does not exist - it just may not be known yet.
Stop "re-inventing theorists" - it's all there
No, no and no.
There is a clear definition of deterministic, random and stochastic quantities.
"Famous mathematician's joke" means that all quantities for which there is no known function that determines their values with 100% accuracy are random or stochastic. This does not mean that such a function does not exist - it just may not be known yet.
Stop "reinventing the theorist" - it's all there
The word 'stochastic' just sometimes replaces 'random'. For example, "random processes" == "stochastic processes"
A deterministic quantity in a theorver, oddly enough, is also a random variable) More specifically, a "degenerate random variable" or "a random variable with a degenerate distribution")
Probability theory, surprisingly, deals with probability theory) It starts with an axiomatic definition of the concept of probability. The concept of a random variable is a derived concept.
My notion of theorver is quite consistent with standard textbooks (Shiryaev's two-volume book, for example), but you have some flight of fancy.)
The word 'stochastic' simply sometimes replaces 'random'. For example, "random processes" == "stochastic processes".
A deterministic value in a theorist, oddly enough, is also a random variable) More specifically, a "degenerate random variable" or "a random variable with a degenerate distribution")
Probability theory, surprisingly, deals with probability theory) It starts with an axiomatic definition of the concept of probability. The concept of a random variable is a derived concept.
My idea of theorver is quite consistent with standard textbooks (Shiryaev's two-volume book, for example), but you have some flight of fancy)
No, no and no.
There are basic definitions in the theorist and no need to make up your own.
And Shiryaev's two-volume book can be thrown at cockroaches.