Zero sample correlation does not necessarily mean there is no linear relationship - page 47
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Quit trading, you're already getting a little nervous.
I may have nerves, but you have something wrong with your head. How can you know in what psychological state I am now, except by hallucinating from your own experience?
Likewise. I should add that, unlike you, my education allows me to understand what I write about and to make a living at it.
Well, it's obvious you know your stuff. And unlike me? Are you hallucinating again? What do you know about me?
Likewise...
Why don't you take the balls off?
However, this does not mean that the QC does not exist - by itself it characterises, I repeat for the third time, the relationship of two random variables at particular moments in time, the same or different (with a shift, that is) for the given two time series. The dependence of QC on the moments t1, t2 for which it is calculated is, by definition, a correlation function.
I do not understand what is the practical value of such a characteristic of 2x CB relationship, if with real independence (KK=0), the correlation function will wobble within such wide limits. It is clear that it is possible to calculate. Here is for example a correlation function for two random walks (I(1)) with mo=0. The original series is divided into non-intersecting parts of 100 samples each. Self-independence and QC=0, and the corr. function:
Corr.function itself freely wanders) between -1 and +1. What does this graph show that is useful for practice? The sample estimates are irrelevant to reality, i.e. it does not show that the series is independent. Is there anything else this function is useful for in practice? What conclusions or results can be drawn?
The reason is that the non-stationarity of the process x2(t) is not taken into account and hence the fact that in this case we cannot take the arithmetic mean over time as an estimate of the mean. Moreover, by construction we know how this average actually changes over time. Therefore the calculation procedure must precisely reduce both parts, on the basis of a priori knowledge of the processes, to a form which permits stationarity to be asserted.
So the only problem is that the arithmetic mean does not reflect the real MO? If for 2 random walks in the QC forum instead of the arithmetic mean is 0 (the real Mo, not its estimate), then the QC will already correctly estimate the "real" correlation?
In mathematics, a process is simply a function of time .
But in theorver (TwiSt) it's something.
When you, dear dear colleagues, will stop quarreling, and just politely agree that to understand each other's theorwers MUST ALWAYS give definitions, because these definitions are different everywhere in the theorwers, then you will be able to understand this hip-hop (Twist is a good classical ballroom dance, and theorwers are monkey hip-hop for fun).
And while you lack the courtesy to agree with each other on definitions, perhaps you might be interested to know who theorvers are worshipping (Kolmogorov's axiomatics, which is actually a tautology).
Here's how Arnold himself - a disciple of the "great" bastard Kolmogorov - recalls Kolmogorovianism:
http://vivovoco.rsl.ru/VV/PAPERS/ECCE/MATH/MATH1.HTM
"ON THE SAD FATE OF "ACADEMIC" TEXTBOOKS
V.I. Arnold,
Academician of RAS, Chairman of Moscow Mathematical Society
I find the experience of writing textbooks for secondary schools by mathematicians of the twentieth century tragic. My dear teacher, Andrey Nikolayevich Kolmogorov, has long persuaded me of the need to finally give schoolchildren a "real" geometry textbook, criticizing all existing ones for leaving such concepts as "an angle of 721 degrees" without a precise definition.
His definition of an angle, intended for ten-year-old pupils, seems to have taken up about twenty pages, and I remember only a simplified version: the definition of a half-plane.
It started with the "equivalence" of complement points to a line in the plane (two points are equivalent if the line segment that joins them does not intersect the line). Then a rigorous proof that this relation satisfies the axioms of equivalence relations; A is equivalent to A, and so on.
A reference to a theorem ( eighty-third, I think) from the previous course then proved that the complement breaks down into equivalence classes.
Several more theorems established successively that "the set of equivalence classes defined by the previous theorem is finite", and then that "the power of the finite set defined by the previous theorem is two".
And finally, the solemnly insipid "definition": "Each of two elements of a finite set, the power of which by the previous theorem is equal to two, is called a half-plane".
The hatred of schoolchildren studying on such "geometry" to geometry and mathematics in general could easily be foreseen, which I tried to explain to Kolmogorov. But he replied with a reference to the authority of Burbaki: in their book "History of Mathematics" (in the Russian translation of "Architecture of Mathematics", edited by Kolmogorov) it says that "like all great mathematicians, according to Dirichlet, always seek to replace transparent ideas with blind computations".
The French text, like Dirichlet's original German statement, stood, of course, for "replacing blind calculations with transparent ideas". But Kolmogorov, he said, found the version introduced by the Russian translator to express the spirit of Burbaki much more accurately than their own naive text, which goes back to Dirichlet. ....."
The example is that the correlation coefficient on a pair of undifferentiated series will tend to unity (for any mu_1 and mu_2 - to sign(mu_1 * mu_2) ) with increasing sample size regardless of the correlation between increments. The whole point is that on the I(1) process the sample mean does not converge to a constant.
The corr. function itself wanders freely) between -1 and +1. What does this graph show that is useful for practice? The sample estimates are irrelevant to reality, i.e. it does not show that the series is independent. Is there anything else this function is useful for in practice? What conclusions or results can be obtained?
What I(1) and I(0) are you talking about for the market?
I(0) is by definition a stationary process. Where is it in the quotes?What I(1) and I(0) are you talking about for the market?
I(0) is by definition a stationary process. Where is it in the quotes?Inmathematics, a process is simply a function of time .
But in theorver (TwiSt), it's something.
When you, dear dear colleagues, will stop quarreling, and just politely agree that to understand each other's theorwers MUST ALWAYS give definitions, because these definitions are different everywhere in the theorwers, then you will be able to understand this hip-hop (Twist is a good classical ballroom dance, and theorwers are monkey hip-hop for fun).
And while you lack the courtesy to agree with each other on definitions, perhaps you might be interested in who theorvers are worshipping (Kolmogorov's axiomatics, which is actually a tautology).
Here's how Arnold himself - a disciple of the "great" bastard Kolmogorov - recalls Kolmogorovianism:
http://vivovoco.rsl.ru/VV/PAPERS/ECCE/MATH/MATH1.HTM
"ON THE SAD FATE OF "ACADEMIC" TEXTBOOKS
V.I. Arnold,
Academician of RAS, Chairman of Moscow Mathematical Society
I find the experience of creating middle school textbooks by mathematicians of the twentieth century tragic. My dear teacher, Andrey Nikolayevich Kolmogorov, has long persuaded me of the need to finally give schoolchildren a "real" geometry textbook, criticizing all existing ones for leaving such concepts as "an angle of 721 degrees" without a precise definition.
His definition of an angle, intended for ten-year-old pupils, seemed to occupy about twenty pages, and I remember only a simplified version: the definition of a half-plane.
It started with the "equivalence" of complementary points to a line in the plane (two points are equivalent if the line segment that joins them does not intersect the line). Then a rigorous proof that this relation satisfies the axioms of equivalence relations; A is equivalent to A, and so on.
A reference to a theorem ( eighty-third, I think) from the previous course then proved that the complement breaks down into equivalence classes.
Several more theorems established successively that "the set of equivalence classes defined by the previous theorem is finite", and then that "the power of the finite set defined by the previous theorem is two".
And finally, the solemnly insipid "definition": "Each of two elements of a finite set, the power of which by the previous theorem is equal to two, is called a half-plane".
The hatred of schoolchildren studying on such "geometry" to geometry and mathematics in general could easily be foreseen, which I tried to explain to Kolmogorov. But he replied with a reference to the authority of Burbaki: in their book "History of Mathematics" (in the Russian translation of "Architecture of Mathematics", edited by Kolmogorov) it says that "like all great mathematicians, according to Dirichlet, always seek to replace transparent ideas with blind computations".
The French text, like Dirichlet's original German statement, stood, of course, for "replacing blind calculations with transparent ideas". But Kolmogorov, he said, found the version introduced by the Russian translator to express the spirit of Burbaki much more accurately than their own naive text going back to Dirichlet. ....."
+5
Our arguments remind me of another picture: the film "Fire, Water and Copper Tubes" - there is a scene where scientists with long beards argue about where the stick ends and where it starts. In the end, their argument ends in a general scuffle, and the solution is actually simple)
It cannot be said better: The conclusion is unambiguous: QC must be calculated on I(0) and only on I(0).
That's right. Good for you. And since I(0) for the price series on the financial markets are not correlated or have extremely low correlation, there is no need to calculate QC at all.
+100 000
And then these people are surprised that they can't make money on forex....