Econometrics: why co-integration is needed - page 22
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Why should having correlation between instruments increase the chances of them converging to zero? The idea is that two correlated random variables will form a third random variable (spread) with each other whose variance will be smaller, but its characteristics will be the same, i.e. we will have the same infinite random walks, albeit on a smaller scale.
We must be talking about different things.
Here's an example, the classic case of arbitrage.
There are two assets, Blue and Green. If we sell at point 1, sell Blue at 6 and buy Green at 2, the profit at point 2 will be equal to 4. This is the simplest case. But when there is an up trend.
Again, it is easy to see that if we buy and sell at point 1, the profit at point 2 will be = 4. In this case, we will of course incur a loss on Blue, but it will be compensated by the profits of Green. The same is true if the coordinated movement of the assets is down.
Nothing changes, the total profit remains = 4. That is why they say that trends do not matter in pair trading. In the simplest case like in the pictures it is true, but in reality not so.
In principle it is, but on the other hand, here is the current situation on these two currencies.
The situations described in the pictures above are also true. The whole issue is to draw the red line competently, the synthetic line.
Let's be specific.
Let's take two pairs. Literally - to me this means that the difference between the two currencies will be stationary, i.e. the mean and variance is a constant. In this case there is a statistical guarantee that the variance between the two currencies will necessarily return to zero. In pictures:
Difference between two currencies
If you draw a bracket, then if it is crossed, you enter, and if it is crossed by zero, you exit.
Here is an idea.
How did the difference between the currencies come about? It's a very serious question, actually.
If this is the difference I was drawing pictures about, then it is very simple. You may enter the market by some sko and exit by zero (this issue was described on the previous page). Or enter by one type of fish and leave by the opposite one. You can think of all sorts of other inputs and outputs on this subject. It depends on the properties of the difference you get.
How did the difference between the currencies come about? This is a very serious question, in fact.
If this is the difference I was drawing about, then it's very simple. You can enter it with some frames and go over zero (it was written about it on the previous page). Or enter by one type of fish and exit by the opposite one. You can think of all sorts of other inputs and outputs on this subject. It depends on the properties of the difference you get.
The properties of the difference are derived from the definition of cointegration:
difference = eurusd - gbpusd * cointegration vector, which is picked up so that the difference is stationary. That is why it is certain that a return to zero is obligatory, just as a transition through zero is obligatory.
Specifically for the above picture:
EURUSD = 0.828446321089*GBPUSD - 1.37009549204 + 0.000206761078317*@TREND
Specifically for the above picture:
EURUSD = 0.828446321089*GBPUSD- 1.37009549204 + 0.000206761078317*@TREND
and it turns out to be an indicator that needs to be reoriented... in practice it is no better than TS on the standard indicator from ta...
although the econometrics is the same
and you get an indicator that needs to be reoriented... in practice it's no better than the TS on a standard ta...
although the econometrics is the same ta...
The properties of the difference are derived from the definition of cointegration:
difference = eurusd - gbpusd * cointegration vector, which is chosen so that the difference is stationary. That is why it is certain that a return to zero is mandatory, just as a transition through zero is mandatory.
I see, if you take out @TREND then we have a simple equation "difference = eurusd - gbpusd * K". Then yes, you play swings, like on a flat, a bounce from the channel boundaries to zero. Only not on the prices themselves, but on their "difference".
Once again, just in case. Declaimer, excuses. No coefficients, no cointegration guarantees that the music will last forever. Due to the very nature of exchange rates. There is no stationarity there in a synthetic instrument (on your trading horizons), no matter what the unit roots tell you about it.
I would like to point out that you simply do not understand anything I write. The inputs and outputs of this TS are based on a stationary series, there are no such indices. You can optimize it or not - it's still not stationary.
It's just a multicurrency one... But that's not the point... The TS will get better on it as you optimize it... i.e. the same classic approach...
cointegration does not guarantee that the music will last forever. Due to the very nature of exchange rates. There is no stationarity there in a synthetic instrument, whatever the singular roots tell you about it.
+1...and there's no difference with ta here...whatever you call it...