Some signs of the right TCs - page 10
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Of course, the direction will change, but not the timing.
With this transformation, indeed, the local extrema will remain in place. Only one function, the ZigZag with a zero min knee, will be able to identify them.
Local extrema identified through a ZigZag with a different size of the min knee (the minimum relative price change between extrema) or non-SigZag (any other function), will not coincide after multiplication by the monotonic function.
The zero ZigZag invariant in your proposed transformation, unfortunately, does not allow for the modified series to return to the original series. Therefore the transformation cannot but change the TC result for all monotone functions.
However, for some specific functions the inverse transformation is possible. I mentioned the function constant. It's quite elementary there.
You pointed to a more general example - multiplication by a linear (in time) function. However, there you need to have at least a small (where there are at least two local extrema) interval of the original price series for an inverse transformation.
At the same time, in reality we do not have such an interval of initial price series. This is even if we leave aside the not entirely clear economic interpretation of such a transformation. Perhaps multiplication by a linear function is a hidden inflation of one of the assets.
All in all, unfortunately, there is no way to generalise about multiplication by a constant. But the idea was very interesting, thank you.
What does ZigZag have to do with it if "...it's about mathematical operations, not computer operations. I.e. One third is one third. The root of PI is the root of PI." The concept of an extremum in mathematics is known to anyone who has graduated from high school and has never heard of Zig-Zag. The monotonic transformation of the y-axis -> F(y) extremum of any continuous function y (x) preserves its x-coordinate since monotonicity is precisely what the inequality y(x1)>y(x2) -> F(y(x1))>F(y(x2)), which lies in the definition of an extremum, preserves justice.
What does ZigZag have to do with it if "...it's about mathematical operations, not computer operations. I.e. one third is one third. The root of PI is the root of PI." The concept of an extremum in mathematics is known to anyone who has graduated from high school and has never heard of Zig-Zag. The monotonic transformation of the y-axis -> F(y) extremum of any continuous function y (x) preserves its x-coordinate since monotonicity is precisely what the inequality y(x1)>y(x2) -> F(y(x1))>F(y(x2)), which lies in the definition of an extremum, preserves justice.
Excellent knowledge of the definition of extremum and monotone function.
Source data for the TS: two numerical discrete series. Not one, but TWO: bid/ask.
ZigZag is a mathematical transformation with these properties:
Excellent knowledge of the definition of extremum and monotonic function.
The topic has slipped from "RIGHT strategies" to "RIGHT mathematical functions"...
My opinion: A RIGHT STRATEGY is a solution in the financial market that allows you to make a STABILIZED PROFIT.
What good is a right function that doesn't make a profit? At best it's a PhD thesis..., and you don't have to be a Trader to do that...
The topic has slipped from "RIGHT strategies" to "RIGHT mathematical functions"...
My opinion: A RIGHT STRATEGY is a solution in the financial market which allows you to make a STABILIZED PROFIT.
What good is a right function that doesn't make a profit? At best it's a PhD thesis..., and you don't have to be a Trader for that...
The point here is that the trading algorithm (TS) is invariant to some transformations of the price (time) function. If we have the right to demand this, then we can check if the Expert Advisors that implement the TS meet these requirements. And we will eliminate in advance all unsuitable ones according to these requirements. Perhaps we will even manage to do something more. At the level of ideas, not Expert Advisors. The ideas should be invariant with respect to the allowable transformations of the price (time) function.
Excellent knowledge of the definition of extremum and monotone function.
Source data for the TS: two numerical discrete series. Not one, but TWO: bid/ask.
ZigZag is a mathematical transformation with these properties:
Not interested in ZigZag in that much detail. Does it really screw up global extrema, keeping only local extrema?
he's just right.
Nikolai, would you show me the final figure,
just a peek at....
I suspect there is one, can't figure it out yet.
The point here is that the trading algorithm (TS) is invariant with respect to some transformations of the price (time) function. If we have the right to demand this, then we can check the Expert Advisors that implement the TS for compliance with these requirements. And we will eliminate in advance all unsuitable ones according to these requirements. Perhaps we will even manage to do something more. At the level of ideas, not Expert Advisors. So that the ideas should be invariant with respect to allowable transformations of the price (time) function.
Very good formulation, thank you!
I was not interested in ZigZag in such detail. Does it really corrupt global extrema, preserving only local ones?
If local extrema are preserved, it is impossible to corrupt global extrema.
The point here is that the trading algorithm (TS) is invariant with respect to some transformations of the price (time) function. If we have the right to demand this, then we can check the Expert Advisors that implement the TS for compliance with these requirements. And we will eliminate in advance all unsuitable ones according to these requirements. Perhaps we will even manage to do something more. At the level of ideas, not Expert Advisors. So that the ideas would be invariant with respect to the allowable transformations of the price (time) function.
Why not start from the main feature - profit? Who needs a correct function, which you have checked, but which does not give profit? Is it a pure science?
Well tie this pure science to the trader's required property - and that property is ONLY profit...!
... tie this pure science to the properties a trader needs - and that property is the ONLY profit...!
When designing a system, we are always dealing with past prices and profits. We need a system which gives profit at unknown prices in the future. What if we happen to have a "tester grail"? A complete answer is impossible in principle. Therefore, the question is modified - how does the system behave at all when there are any changes in the price series?