Theorem on the intersection of two MAs
Is any of this correct?
1 and 2 are tautologies. And true or not, without mathematical proof, just a private opinion. And to construct a proof base without seeing the practical application, I don't see the point... Maybe you can share the point?
1. For any time interval it is possible to choose such parameters (optimization) that the Expert Advisor will give profit on their basis.
In other words, there is no interval, on which the optimization will not give results.
2) Any timeframe can be divided into a finite number of parts, so that after the optimization the Expert Advisor will be profitable at each part of it.
Hmmm...
Is any of this correct?
That's right. Fitting is called, if I'm not mistaken.
There is a kind of cyclicality in the market - a kind of cycle. This cycle is constantly changing. But not immediately, but over time. If you calculate it, then MA crossings work very well. So the problem is to correctly find this future market cycle using only historical data, understanding that tomorrow this cycle may change - in simple terms - how to correctly optimize TS on historical data, to find the market cycle that will be tomorrow......)))))
There is a kind of cyclicality in the market - a kind of cycle. This cycle is constantly changing. But not immediately, but over time. If you calculate it, then MA crossings work very well. The problem is to correctly find this future market cycle using only historical data, knowing that tomorrow this cycle may change - in simple terms - how to optimize TS on historical data, to find the market cycle that will be tomorrow......)))))
LeoV, are you alluding to the works of John Ehler or some other original method?
Well, of course him too - many people try to calculate this market cycle and in different ways..... I meant the TS with MA crossings - it is the simplest model of the market using its cyclic behavior.
1 and 2 are tautology. And right or wrong, without mathematical proof, just a private opinion. And to construct a proof base without seeing the practical application, I don't see the point... Maybe you can share the meaning?
Not a tautology. 1 means that you can always pick up such a 1(one) set of parameters. mashek that will be profitable at any period, including all from 99 to 2009.
But for example from 99 to 2010 the set will be different.
And 2 - it is impossible to do with one set, but in principle it is always possible to optimize, and there will be no segments, on which the loss is inevitable.
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You can use any "good" indicator with a limited set of optimizable parameters. A "good" indicator means working in principle, not just any piece of code.
In other words, the picture of the black box is as follows - we seem not to see the price series itself, we see only indicator parameters and optimization results - profits or no profits.
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An indicator is a certain mathematical operator that is applied to the price series. Then if there is a profit for a period - it can be said that the market is characterized by several parameters at this period. Just like a thermometer measures the air temperature, but not the speed of single molecules and therefore the air has a macro parameter - temperature. That is, from statistical mechanics we have moved on to thermodynamics.
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The next question is whether these parameters can be calculated for a given indicator directly from the price series instead of the tester's optimization. Then we can shove these calculations into the Expert Advisor
and recalculate the profit parameters on the fly.
There is a kind of cyclicality in the market - a kind of cycle. This cycle is constantly changing. But not immediately, but over time. If you calculate it, then MA crossings work very well. So the problem is to find this future market cycle correctly, using only historical data, understanding that tomorrow this cycle may change - in simple terms - how to optimize the TS on historical data, to find the market cycle that will be tomorrow......)))))
You are absolutely right ;))
Again there is the question of cycle lifetime. The cycle parameters won't change with the arrival of the next tick, will they? How many ticks should pass before these parameters are no longer profitable?
This can also be a market characteristic.
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It is clear that it may be zero ticks, i.e. we optimized on the nearest history from the first to the N-th bar, started to work, and from the zero bar we immediately went to the loss.
Again, this raises the question of cycle time.
What you are trying to formalise here is called the stationarity of a parameter in some process. In this case we are talking about stationarity for one of the harmonics, if the cotier is considered as a set of harmonic signals.
Indeed, the difference of the two sweeps (see your first post), is almost the first derivative of the higher muve. The bandwidth of an ideal digital differential operator is a straight line drawn from the origin (y=f) and ending at the Nyquist frequency (or 1/2 of it, can't remember) on the abscissa axis, which corresponds to a double TF and 1 on the ordinate axis. Given that in the first approximation the cotier spectrum is proportional to 1/f, we obtain a window in the entire frequency range where all harmonics of the original BP are represented by a weight of 1. Thus, optimizing such RT on historical data using your proposed algorithm will only identify the harmonic with the maximum amplitude. And everything would be fine, but for one BUT - the position of such harmonic is not stationary in principle. Therefore, to build a profitable TS using two muves conversion is impossible - the optimization parameter is not stationary.
If we use several muves with different smoothing periods in TS and define the signal to buy as a weighted sum of signals from each crossover, we will get a trivial Fourier analysis. The world is one again in all its manifestations!
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1. For any time interval it is possible to choose such parameters (optimization) that the Expert Advisor will give profit on their basis.
In other words, there is no interval, on which the optimization will not give results.
2) Any timeframe can be divided into a finite number of parts, so that after the optimization the Expert Advisor will be profitable at each part of it.
Hmmm...
Is any of this correct?