Zero sample correlation does not necessarily mean there is no linear relationship - page 55
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You're stressing the point, but meanwhile you have lost it yourself. A simple example, two stationary, random walks with zero MO:
It is obvious that both are pointing in the same direction, it is also obvious that there is no relationship between these processes. Taking the QC for the two series as it is, we get a coefficient of 0.86, i.e. we have identified a strong relationship. But if it is reliably absent, then what have we got? Now we take the first differences of these two processes and calculate the correlation coefficient for them and now it is equal to 0.02, i.e. it has shown what it should show - there is no connection. Their movement in one direction is a simple coincidence.
By calculating QC on I(1) you are fitting statistical methods to what seems to you. And visually, the two series do appear to be similar, when in fact they are not.
Don't call a correlation what it is, and don't give correlation properties that it doesn't have.
Guys, you've made your point. Enough of this, no need to quote me, let alone teach me, I do not participate in the correlation threads here any more.
A very good example, thank you. A pebble in the direction of lovers of false correlations who think they will never get it.
That's a good pebble to have on your head. Who came up with the concept of false correlation? There's a tendency - when someone doesn't understand something, they come up with new definitions and concepts. You make up your own expectations of correlation, then start making up new definitions when expectations are not met. Once again - in mathematics, as it turns out, it's not enough to manipulate formulas, you still need to understand the essence.
That's a good pebble on the head. Who came up with this notion of "false correlation"? There's a tendency - when someone doesn't understand something, they come up with new definitions and concepts. You make up your own expectations of correlation, then start making up new definitions when expectations are not met. Once again - in mathematics, as it turns out, it's not enough to manipulate formulas, you still need to understand the essence.
Just for the sake of the truth my three cents.
False correlation is exactly from the textbook, literally on the first 10 pages of the correlation analysis textbook.
The next 10 pages of that textbook say that a false correlation can only be distinguished from a true correlation by meaningful reasoning.
I apologise if, what, as you are to be both disagreed with and agreed with.
Correlation is not used in economics. To avoid using correlation, Granger got a Nobel for cointegration 30 years ago. Much less error in application. It is on cointegration that various VARs, VECs are built, portfolios are formed, risks are managed, etc. A whole direction. Any econometrics package has all this stuff.
Just for the sake of the truth my three cents.
False correlation is exactly from the textbook, literally on the first 10 pages of the correlation analysis textbook.
The next 10 pages of that textbook say that a false correlation can only be distinguished from a true correlation by meaningful reasoning.
I apologise if, what, as you are to be both disagreed with and agreed with.
Correlation is not used in economics. To avoid using correlation, Granger got a Nobel for cointegration 30 years ago. Much less error in application. It is on cointegration that various VARs, VECs are built, portfolios are formed, risks are managed, etc. An entire field. Any econometrics package has all this stuff.
Don't call correlation what it is, and don't give correlation properties that it doesn't have.
Guys, everything is clear with you already. Enough of this, don't quote me, let alone lecture me, I don't participate in correlation topics here anymore.
I don't know what you mean. "Correlation is not what it is...", some "properties it does not possess".
You tell me clearly and distinctly, is there a correlation between the two series that I presented above, or is there not?
1. MO=0? MO of rows = 0? Or the primes of the series?
2. both series are stationary? Are you sure about that?
3. QC does not and never has established the presence or absence of any functional relationships. It is simply a numerical characteristic. The presence or absence of relationships is a matter of QC interpretation by other methods.
On wikipedia it says, and I quote: "Stationarity of a random process means that its probability patterns are constant over time, with two kinds of stationarity usually considered: stationarity in the narrow sense, where finite-dimensional distributions are invariant with respect to time shifts, and stationarity in the broad sense, where only the mathematical expectations do not depend on time." There is not a single word about the fact that the MO must be strictly equal to zero, and that stationarity is only a property of I(0).
On wikipedia it says, and I quote: "Stationarity of a random process means that its probability patterns are constant over time, with two kinds of stationarity usually considered: stationarity in the narrow sense, when the finite-dimensional distributions are invariant with respect to time shift, and stationarity in the broad sense, when only the mathematical expectations do not depend on time." There is not a single word about the fact that MO must be strictly equal to zero, and that stationarity is only a property of I(0).
Well, that's right - your MO of the rows is growing (or dropping - I can't figure out where the time is in this coordinate system) over time. Split the series into two parts, the MO of the second part is clearly greater than the first. These are not stationary series.
If you meant stationarity of series from first differences, you should have posted graphs of first differences.
I don't know what you mean. "Correlation is not what it is...", some "properties it does not possess".
You tell me clearly and concisely, is there a correlation between the two rows I presented above or not?
There are all kinds of correlations. And that there is a correlation, you know that.
...
False correlation is exactly from the textbook, literally in the first 10 pages of a textbook on correlation analysis.
...
In such cases, you need the exact name of the textbook, the author. Maybe there is something else funny in it.
In such cases, you need the exact name of the textbook and author. Maybe there is something else funny in it.