Zero sample correlation does not necessarily mean there is no linear relationship - page 48
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There is no better way to put it: The conclusion is unambiguous: you should count QC on I(0) and only on I(0).
(It's about time we slowed down this run into the woods...) Let's be down-to-earth.
The problem is that you are dancing the TwiSt sloppily. You throw around formulas, words, definitions and conclusions carelessly.
Who "needs"? You personally? Or "in general, always" or "for the time series"?
In the science of TwiSt (in Carl's time, well Pearson) there was not and is not a single unified methodology for solving problems similar to what is found in other numerical methods. TwiSt has a set of methods, most of which are reliably applicable to random variables which are normally distributed, according to Carl (Gauss). So it doesn't just matter which formula to shove the measurement results into, it also matters WHAT BOTH logically related reasoning goes along with those calculations. That's the "problem" of modern theorizing.
TwiSt science simply tests hypotheses. And in order not to lose this very hypothesis in the course of reasoning - it is necessary that the WHOLE, I repeat the WHOLE chain of calculations be double-checked for consistency with the set OBJECTIVE (and hypothesis).
Formulate the hypothesis, AND the OBJECTIVE. What is your hypothesis? That there is a connection between the rows? Let us suppose. What is your goal? What decision(s) do you intend to make when the next bar comes in? What should the chain of accounts tell you? That there was no connection and it appeared? Or that it was small and it became big? If you do not check with the hypothesis and with the goal, the chain of arithmetic you have constructed may contain a flaw, or a hasty conclusion, or too general a conclusion, and it will lead to an error.
That's right. Good for you. And since I(0) for price series in financial markets are not correlated or have extremely low correlation, QC should not be counted at all.
...
That's not true. The correlation will be significant. If you get to the bottom of the QC formula, you will realize that the probability of unidirectional increments on a segment where both processes go in the same direction will be higher than 50/50.
on a segment, yes. For any increment I can find a segment where KK is close to +1. Or I can find a segment where KK is close to -1. Or I can find a segment that is close to 0.
That's just the way it is.
(It's about time we slowed down this run into the woods...) Let's be down-to-earth.
The problem is that you are dancing the TwiSt sloppily. You throw around formulas, words, definitions and conclusions carelessly.
Who "needs"? You personally? Or "in general, always" or "for the time series"?
In the science of TwiSt (in Carl's time, well Pearson) there was not and is not a single unified methodology for solving problems similar to what is found in other numerical methods. TwiSt has a set of methods, most of which are reliably applicable to random variables which are normally distributed, according to Carl (Gauss). So it doesn't just matter which formula to shove the measurement results into, it also matters WHAT BOTH logically related reasoning goes along with those calculations. That's the "problem" of modern theorizing.
TwiSt science simply tests hypotheses. And in order not to lose this very hypothesis in the course of reasoning - it is necessary that the WHOLE, I repeat the WHOLE chain of calculations be double-checked for consistency with the set OBJECTIVE (and hypothesis).
Formulate the hypothesis, AND the OBJECTIVE. What is your hypothesis? That there is a connection between the rows? Let us suppose. What is your goal? What decision(s) do you intend to make when the next bar comes in? What should the chain of accounts tell you? That there was no connection and it appeared? Or that it was small and it became big? If you do not check with the hypothesis and with the goal, the chain of arithmetic you have constructed may contain a flaw, or a hasty conclusion, or too general a conclusion, and it will lead to an error.
on a segment, yes. For any increment I can find a segment where KK is close to +1. Or I can find a segment where KK is close to -1. Or I can find a segment that is close to 0.
It's just a matter of figuring it out.
Sine and cosine go in ONE direction on some segments. That is, their linear correlation on a short segment will be greater than zero:
(this figure was above in this thread)
.... And then they go in different directions. Therefore, when CONNECTED on the long segment, it turns out that the correlation between them is zero and they are considered orthogonal. This is the kind of contradiction which stems from the fact that all resources are finite and the main resource is the length of the measurement segment, i.e. time.
(It's time to slow down this entry into the woods...) Let's talk down-to-earth.
The problem is that you are dancing the TwiSt sloppily. You are sloppily throwing around formulas, words, definitions and conclusions.
Who "needs"? You personally? Or "in general, always" or "for the time series"?
In the science of TwiSt (in Carl's time, well Pearson) there was not and is not a single unified methodology for solving problems similar to what we have in other numerical methods. TwiSt has a set of methods, most of which are reliably applicable to random variables which are normally distributed, according to Carl (Gauss). So it doesn't just matter which formula to shove the measurement results into, it also matters WHAT BOTH logically related reasoning goes along with those calculations. That's the "problem" of modern theorizing.
TwiSt science simply tests hypotheses. And in order not to lose this very hypothesis in the course of reasoning - it is necessary that the WHOLE, I repeat the WHOLE chain of calculations is rechecked for compliance with the set OBJECTIVE (and hypothesis).
Formulate a hypothesis and also a goal. What is your hypothesis? That there is a connection between the rows? Let's say. What is the goal? What decision(s) do you intend to make when the next bar comes in? What should the chain of accounts tell you? That there was no connection and it appeared? Or that it was small and it became big? If you don't check with the hypothesis and with the goal, the chain of arithmetic you build may contain a flaw, or a hasty conclusion, or too general a conclusion, and it will lead to an error.
So if you have any knowledge of causal methods, please speak up, I have a complete blank on the subject.
The best known approach is the Granger causality test. You can also look at transfer entropy
By the way, you are getting ahead of yourself here, that the presence of correlation does not mean causation - that is clear to me too. But we have to start somewhere. So far I use cross-correlation - I don't know/understand other methods. So if you have knowledge about methods of establishing causal relationships please speak up, I have a complete gap in this subject.
No problem. Let's just be clear about the motivation, or rather the difference in motivations. You, my colleague, as a practicing trader, look for connections in price series charts, (by looking at them or not) calculate cross-correlations and conclude from further movement of ONE currency that the OTHER currency, which has not yet moved, but which is RELATED to the first, is also MOVING. And then you decide to open a position - to make money on the price movement. Right? If so, that is your HYPOTHESIS in a probabilistic sense.
Well, it's a pretty decent thing to do these days.
That's how traders at big banks and hedge funds work.
(I'll find the links in a moment).
But it's so to speak a BULLY PRACTICAL APPROACH. Weren't you in the thread ". PRGP"? There I quoted Carl (well Pearson), who says that it is OK to do so, but there are no guarantees of such a method (well, more precisely, that is Carl personally and his friend Yul).
But personally, I believe that most qualified mathematicians on this forum are NOT particularly interested in special cases of such correlations. They are interested in statistical trading models in general, for all occasions.
At least I personally draw this conclusion from messages like Alsu, Gpwr, Reshetov, Integer, Neutron, faa1947, Privalov and others, sorry in advance if I haven't clearly indicated anyone in this "quick list".
Therefore, in order to interest them, to get answers to their questions, these questions must be formalized, and the problem is that for a substantive conversation the wording must be STRICT.
No problem. Let's just be clear about the motivation, or rather the difference in motivations. You, my colleague, as a practicing trader, look for connections in price series charts, (by looking at them or not) calculate cross-correlations and conclude from further movement of ONE currency that the OTHER currency, which has not yet moved, but which is RELATED to the first, is also MOVING. And then you decide to open a position - to make money on the price movement. Right?
Well, it's a pretty decent thing to do these days.
That's how the traders of the big banks and hedge funds work.
(I'll find the links in a moment).
But it's so to speak a VERY PRACTICAL APPROACH. Weren't you in the thread ". PRGP"? There I quoted Carl (well Pearson), who says that it is POSSIBLE to do so, but no guarantees of such a method (well, more precisely, that is personally Carl and his friend Yul).
But personally, I believe that most qualified mathematicians on this forum are NOT particularly interested in special cases of such correlations. They are interested in statistical trading models in general, for all occasions.
At least I personally draw this conclusion from messages like Alsu, Gpwr, Reshetov, Integer, Neutron, faa1947, Privalov and others, sorry in advance if I haven't clearly indicated who in this "quick list".
Therefore, in order to interest them, to get answers to their questions, these questions must be formalized, and the problem is that for a substantive conversation the wording must be STRICT.
On the whole, yes, that's true. But with the only exception that I need methods that allow me to determine the connection, rather than using the assumption that there is such a connection a priori. For example, I read an article on regression analysis on wikipedia:
OK, so before we use the same regression analysis we have to identify the relationship. But how do we do it? We can't do it with regression analysis because it is a consequence of the relationship, we can't do it with correlation because QC itself doesn't talk about cause-effect relationships, and we can't do it with cross-correlation? - seems to be better, but that's where my knowledge ends...