Econometrics: why co-integration is needed - page 11
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In that case, the non-stationarity of the two series must be identical, so that it (non-stationarity) is extinguished by subtraction.
If it is different, then after subtraction we get third kind of unsteady series.
How, by what parameters can we compare non-stationarity of two non-stationary series?
what does it mean that the non-stationarity is identical?
Equivalent. That is, the two series are moving according to the same laws. Then if you subtract them, you get a stationary series - the non-stationarity is compensated.
Equal. That is, the two series move according to the same laws. Then if you subtract them, you get a stationary series - the non-stationarity is compensated for.
How so? Two rows moving according to the same laws are two identical rows? And how do you "subtract the laws"?
The return time is also estimated from the stationary series itself. It is usually distributed according to not very nice exponential type laws.
Stat.arb. has been around for decades and there are serious works.
I don't know the answer to this question myself. But faa1947 subtracts one non-stationary series from another non-stationary series and gets a stationary series. So it is possible to conclude that the two series move by the same laws since the non-stationarity has been compensated by subtraction.
I don't know the answer to this question myself. But faa1947 subtracts one non-stationary series from another non-stationary series and gets a stationary series. So it is possible to conclude that the two series move according to the same laws since the non-stationarity has been compensated by subtraction.
Not exactly subtracting.
I am aware of two approaches to cointegration:
(1) regression cointegration
(2) panel cointegration testing
The first one is used in this topic. The goal is to obtain the cointegration vector. It is estimated and given on the first page of the topic. If we multiply by this vector all regression terms, in our case the left side for which multiplier = 1, and the right side is three terms (see page 1), and then subtract from the right side the left side, we obtain a stationary series. This can be done if the integration of the series is the same. So there is no need to say "subtract and obtained". There are conditions of equality of integration and as far as I understood there may be more than one vector. Now I can't remember if we can always get a vector.
Stat.arb. has been around for decades and there are serious writings.
But then the next question appears - if two series have moved the same way in the past, according to the same laws, then where are the guarantees that they will move in the future in the same way, in the same way? )))
My experience is that the integration of the eurusd series has changed. I do not know if the integration of the index series has changed in the same way. If it has not changed, then there will be no cointegration.
what does non-stationarity mean identical?
Equal integration. What is meant here is the following. We differentiate a quotient - we take the difference of neighbouring bars. If we got a stationary series, then the original series is integrated and is written I(1). If we had to differentiate twice - I(2) etc. Seen up to 5. This procedure is the unit root test. We check the original quotient - level. Then the differences are in order.