Econometrics: one step ahead forecast - page 91
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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
1. No one ever said that it is impossible to earn in nonstationary conditions.
2) It is possible to determine whether the sum of series of 100 takes will be stationary or not, only after analysis of a generated series. Examples with virtual coins told "on the fingers" and with doubtful conclusions is better not to apply. Take a non-stationary time series of EURUSD prices, show there "quasi-stationarity" and a way to profit.
3. TS cannot be stationary or non-stationary, time series can be stationary and non-stationary. A TS can have a positive or negative profit MO.
there is no circle)) If you want to use the tests and hope to see something similar in the real world, quasi-stationarity is needed. If it is not there, the tests are useless - we will not get anything like that in the real world.
Tester tests? I don't use them, because "it's a fraud" :)))
But after the tester there is no, will not and cannot be any confidence, no matter what kind of stationarity it may give me.
I prefer to test it in the flesh - it takes longer, but you can see the real situation, not the tester cheat.
For example, all December I will show daily "live" the results of last modification of my tractor - you may watch it if you're interested
http://www.procapital.ru/showthread.php?t=41961
News leading to "sudden and unpredictable" changes doesn't happen that often. Anyway, 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 place 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 prediction.
"Sudden and unpredictable" is not necessarily the result of news.
And if you look at the quote you do see "stable and long enough", the only problem is that once they become long enough, they change direction (trend) for some reason - that's non-stationarity. The best point to determine the past trend is the point of extremum.
" non-stationarity does not exist at all, but partially " and " non-stationarity of the residual " is unclear. The non-stationarity of the time series is clear, but why would you want non-stationarity of the residual?
1. No one has ever said that you can't make money in non-stationary conditions.
2. whether or not the sum of the series of 100 throws will be stationary can only be determined after the analysis of the generated series. Examples with virtual coins told "on the fingers" and with dubious conclusions are better not to apply. Take a non-stationary time series of EURUSD prices, show there "quasi-stationarity" and a way to profit.
3. TS cannot be stationary or non-stationary, time series can be stationary and non-stationary. TCs can have positive or negative MO of profit.
1. many have said and are saying, but that is not what I wrote about
2. who says the coin example has to be applied? As for taking you and showing you something, I'm not hired actually))
3. take the returns of the system - it is the same series and it can be either stationary or non-stationary. It makes sense to talk about mo returns for stationary, or at least quasi ;)
http://www.procapital.ru/showthread.php?t=41961
ok
3. take the returns of the system - this is the same series and it can be stationary or non-stationary. It makes sense to talk about mo profit for stationary, or at least quasi-stationary ;)
What is "system returns"?
What is "system returns"?
the results of trades as well as series of trades
the results of trades as well as series of trades
So the profit stream produced by the TS can also be stationary or not? And if it is non-stationary - should the profit be recognised as unsteady?
"Sudden and unpredictable" is not necessarily the result of news.
And if you look at the quotient you really see "stable and long enough", the only problem is that once they become long enough, they change direction (trend) for some reason - that's what non-stationarity is. The best point to determine the past trend is the point of extremum.
" non-stationarity does not exist at all, but partially " and " non-stationarity of the residual " is unclear. The non-stationarity of the time series is clear, but why would you want non-stationarity of the residual?
So can the profit stream generated by the TC also be stationary or not? And if it is non-stationary - recognise the profits as unsteady?
random.