Zero sample correlation does not necessarily mean there is no linear relationship - page 45
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What's the point of these constructions anyway, QC - it characterises the relationship of two random variables, and at a given moment in time, not over any interval. The latter is true only if the two processes being compared are a) stationary b) ergodic, which is absolutely not the case for the given functions, hence the sample QC as an estimate of true QC makes no sense at all for them. In other words, one must first prove (or at least reasonably assume) stationarity and ergodicity, and only then substitute the series into the formula.
I always thought the QC counted for the period........... What do you mean, per period?
Why stationarity and ergodicity?
First they demanded normality, now stationarity and ergodicity.....
See my previous post - if on an interval where we can approximate conditions a and b
It's not like that. Going deep into some Amazon wilderness.... In simple terms - the correlation coefficient shows how similar one curvature is to another. What the moon and the saucer are identical because they're round, etc. The correlation coefficient compares shape without regard to size. That's it. Nothing else. Everything else they say about correlation coefficient is heresy.
I always thought the QC counted for the period........... What do you mean by period?
It's not like that. Going deep into some Amazon wilderness.... In simple terms, the correlation coefficient shows how much one curvature is similar to another. What the moon and the saucer are identical because they're round, etc. The correlation coefficient compares shape without regard to size. That's it. Nothing else. Everything else they say about correlation coefficient is heresy.
the definition of QC states that it describes the relationship between two random variables. If we are dealing with processes - we are thereby considering different random variables at each point in time. And only if they have time-consistent distribution parameters (stationarity) can we calculate QC from a sample by replacing the ensemble mean (which is in the formula for Pearson's linear QC, for example) by the time mean (ergodicity). This is not heresy, but a precise work with the definitions of the concepts and as a consequence the meaning of the formulas.
As for the similarity of the two curvatures, the concept of a correlation function applies to them, which at point 0 gives the very correlation coefficient. And the same restrictions apply to the validity of its estimation as to the correlation coefficient - the requirement to assume stationarity and ergodicity of the sample in question. This is not a whim, but a necessity; without it all estimation formulas lose their meaning.
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In order to calculate kc, you have to put the numbers in the formula and nothing else. If the coefficient is 1, then the shape is identical (the size may be different), if -1 is a mirror image, 0 is not similar at all. The correlation coefficient does not show anything else and calculation of correlation has nothing to do with normality or ergodicity and stationarity. What kind of textbooks are you reading?
In order to calculate kc, you have to put the numbers in the formula and nothing else. If the coefficient is 1, then the shape is identical (the size may be different), if -1 is a mirror image, 0 is not similar at all. The correlation coefficient does not show anything else and calculation of correlation has nothing to do with normality or ergodicity and stationarity. What kind of textbooks are you reading?
Reading. The correlation coefficient is defined for random variables. In the formula are random variables. The figure shows random processes. In order to put random processes into the formula for random variables, specific conditions must be met. If they are not satisfied, the formula cannot be substituted. It is as simple as two kopecks.
Where does it come from? Where did you read that?
the definition of QC states that it characterises the relationship between two random variables. If we are dealing with processes - we are thereby considering different random variables at each point in time. And only if they have time-consistent distribution parameters (stationarity) can we calculate QC from a sample by replacing the ensemble mean (which is in the formula for Pearson's linear QC, for example) by the time mean (ergodicity). This is not heresy, but a precise handling of the definitions of the concepts and as a consequence the meaning of the formulas.
As for the similarity of the two curvatures, the notion of a correlation function applies to them, which at point 0 gives the very correlation coefficient. Moreover, the same restrictions apply to the validity of its estimation as apply to QC - the requirement to assume stationarity and ergodicity of the sample in question. This is not a whim but a necessity; without it all estimation formulas lose their meaning.
Where did that come from? Where did you read that?
A definition of the correlation function can be found in any TV&T textbook. The notion of a random process does not appear in it. The definition of a random process is also in textbooks: a SP is a time-ordered (discrete or continuous order) sequence of random variables.
I still don't get it)) for I(1) QC is valid?
Yes, it is valid, but estimating its usual formula for a sample linear QC is invalid because the series is non-stationary: the mean, which is included in the formula, is not a constant over the sample, it depends on time. For a stationary series, the mean is constant over time, and we estimate it simply by replacing it with the arithmetic mean; for i(1) this is quite obviously incorrect.
However, this does not mean that QC does not exist - by itself, I repeat for the third time, it characterises the relationship of two random variables at particular points 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.
The definition of CC is in any textbook on TV&T. The concept of a random process does not appear in it. The definition of a random process is also in textbooks: a SP is a time-ordered (discrete or continuous order) sequence of random variables.
Don't talk about any one, be specific, the name of the textbook, a quote from it with a definition. Even if you are sure you have understood the definition correctly, how can you be so sure? Have not tried with your own hands to feel the correlation coefficient (to experiment, play), to understand, realize, feel what it is?
How is it possible to get so caught up in it?
I don't know what a twist is (unless it's some kind of dance), looked up the definition of correlation on wikipedia:
Correlation (from Latin correlatio - correlation, relationship), correlation dependence is a statistical relationship between two or more random variables (or variables that can be considered as such with a certain acceptable degree of accuracy).
Are you trying to critique what's written on the fence somewhere? What does this have to do with random variables? Only some asshole could have written that definition. If in all textbooks on hip-hop or whatever it is it's the same, then all these textbooks were written by assholes who don't understand what correlation is and fuck up the brains of students themselves.