Econometrics: one step ahead forecast - page 90

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You can, of course, take a price series as "piecewise stationary", you can endlessly transform a price series in the hope that the n-th conversion will produce a stationary series - all this is pure shamanism.

With any method the price is subject to "sudden and unpredictable" changes - this is the notorious non-stationarity

 
avtomat:
It is necessary to separate what can be from what should be.

In any case, it is desirable that the system returns are close to stationary and match the test returns. Especially in a series of trades. If you initially believe that this is not the case, then you can disregard the results of historical tests. I.e. quasi-stationarity of results of a series of trades is still needed.
 
Avals:

in any case, it is desirable that system returns are close to stationary and match test returns. Especially in a series of trades. If you initially believe that this is not the case, then you cannot trust the results of historical tests - you can just disregard them. I.e. quasi-stationarity of results of a series of trades is still needed.
going around in circles...
 
Does anyone else remember what a Soviet-era mechanical scale looks like? There is a set of weights. There is an item to be weighed. Would anyone bet 5 kopecks that in the process of selecting the weights and weighing (to be weighed in the minimum number of attempts), an "overweighting of the weights" will occur? What would you have to do, in such a case, to establish equilibrium? The scales may be different, the weights may be different... but the approach is the same...
 

>
 
"for speed"... so to speak...
 
avtomat:
walking in circles...

there is no circle)) If you want to use tests and hope to see something similar in the real world, then quasi-stationarity is needed. If you don't, you don't need the tests - you won't get anything like that in the real world.
 

Here is a simple example of stationarity, non-stationarity and how you can make money in a non-stationary environment.

We have the right coin and the person who flips it. An ideal mathematical abstraction is the probability of heads/tails=0.5/0.5. Let heads=+1 and tails=-1. The distribution of the individual outcomes is binary. But if we take for example sum of 100 rolls, it will be distributed normally with mo=0, sko=50. Stationary distribution, you can't make any money.

Now the tosser has not one coin, but many, and some of them are wrong with different probability shifts in favour of heads or tails. And the tosser changes the coin tossed to any coin from this set. The distribution is also binary. The sum of a series of 100 tosses will not be stationary. Watching and calculating statistics for the previous 100 or more flips does not guarantee that the flip of a coin will not change. Another thing is if for example it is observed that the flip of a coin is more often than every 200 tries, or after getting more than five heads or tails in a row. Then on the basis of this information a system can be constructed which returns are quasi-stationary. The system will work as long as the shooter follows similar rules. And it is not necessarily related to his will, but for example simply to external circumstances, or constraints. It is possible to find stationary characteristics on non-stationary process and use them.

I.e. non-stationarity of a quotient does not mean that all systems built on it will be non-stationary. If it is so, then there is no sense to build a system on historical data at all. Quasi-stationarity of some market properties is enough

 
Avals:

Actually, imho there is a winning strategy in any case if there is at least one wrong coin ;)

Shit, although no, it depends on the rules.

 
Demi:

You can, of course, take a price series as "piecewise stationary", you can endlessly transform a price series in the hope that the n-th conversion will produce a stationary series - all this is pure shamanism.

With any method the price is subject to "sudden and unpredictable" changes - this is the notorious non-stationarity

News that leads to "sudden and unpredictable" changes does not happen very often. In general, it's a matter of faith: I look at the kotir and see steady and fairly long term directional movements. And on all timeframes. It is the presence of trendiness in the market that determines the possibility to predict. In the kotir transformations we're trying to get to the point where it is pure, so to say, having determined the trendiness in the analytical form. And consideration of non-stationarity of the residual is the quality of market trend forecasting.
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