Zero sample correlation does not necessarily mean there is no linear relationship - page 44

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Demi:

Let's have a look together:

There is my post "CC MAY and MUST be counted by the original rows." Now pay attention, question - is there the word ONLY in the meaning of "CC MAY and MUST be counted ONLY by the original rows"?))

Then why do you write me: "again, what is the argument about - CC MAY and MUST be counted by original rows"? That's what I'm discussing)))
 
C-4: Can you provide a concrete example where taking logarithms changes the QC readings in a key way? I please an example where the original series gives a QC close to zero, while its logarithms miraculously put the QC at a meaningful estimate.

OK, take the two orthogonal functions sine and cosine. Obviously, the correlation between their values is zero.

Now let's change these functions a bit to make them more like a price series: 1) let's raise them above zero 2) and gradually increase the values according to the relative scale using the exponential function.

We measure Pearson's QC for the values obtained, and for their logarithms. The QC for logarithms tends to zero. The QC calculated "head-on" indicates the existence of a relationship. What is the QC to which you are referring?

The example is far-fetched and does not quite fit your query, but still.

 
GaryKa:

OK, take the two orthogonal functions sine and cosine. Obviously the correlation between their values is zero.

Why?

Do you even understand what "The correlation between their values is zero" means? This expression means that KK=0, which is not the case (and this can even be determined visually).

 
Demi: Why? Do you even understand what "Correlation between their values is zero" means? This expression means that CC=0

I don't even know what to say (I thought I mentioned orthogonality). Why? Because that's the nature of it.


Here's the excel file, experiment.


Demi: ... This expression means that KK=0, which is not the case (and this can even be determined visually).

Perhaps this is the conclusions from a visual comparison that spawned this topic.

Files:
pirson.zip  16 kb
 
GaryKa:

Which correlation coefficient will you use?


If you want to know the correlation coefficient, you will use the correlation coefficient. If you want to know the correlation coefficient, you will have to look at the correlation coefficient.

First you have to determine what you are walking on and then apply either a correlation coefficient, or a correlation coefficient for the difference or the logarithm or whatever, or maybe not a correlation coefficient at all.

 
Good example with sine and cosine. The correlation is a hundredfold and the correlation value is 0. You just need to understand what the correlation coefficient shows and not give it properties that it does not have.
 
GaryKa:

I don't even know what to say (I thought I mentioned orthogonality). Why? Because that's the nature of it.

Here's the Excel file, experiment.

Perhaps these are the conclusions from a visual comparison that spawned this thread.

Yes? And I was once taught that the correlation coefficient of cosine and sine varies smoothly from -1 to +1. Turns out it's 0........
 
Demi:
Yes? And I was once taught that the correlation coefficient for cosine and sine varies smoothly from -1 to +1. Turns out it's 0........


It depends on what period to count. If it is shorter than the period of sine and cosine, it goes this way and that way. If exactly the period of sine and cosine, 0.
 
GaryKa:

OK, take the two orthogonal functions sine and cosine. Obviously, the correlation between their values is zero.

Now let's change these functions a bit to make them more like a price series: 1) raise them above zero 2) and gradually increase the values according to the relative scale using the exponential function.

We measure the Pearson QC for the values obtained, and for their logarithms. The QC for logarithms tends to zero. The QR calculated "head-on" indicates the existence of a relationship. What is the QC to which you are referring?

The example is far-fetched and does not quite fit your query, but still.


What is the point of these constructions, the QR describes the relationship between two random variables at a given moment in time and not during an 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.
 
Integer:

It depends on what period to count. If it is less than the period of sine and cosine, it goes this way and that way. If exactly for the period of sine and cosine, 0.

See my previous post - if on an interval where we can approximate conditions a and b
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