Ok, here is a question you can't answer. How do you solve a math equation where the elements of that equation are not stable, they are constantly & ever changing?
I think that's called non-stationary statistics. I cut the Gordian Knot with backtesting that merges it all together. Neither are the results stationary, but they suffice to make pocket change and to keep an old man out of trouble.
I would never say I am a better trader than anyone else. There are too many edges out there to profit from. People use edges that I look at and am amazed at their unstable foundation but they still trade them profitably. Posted is a eMini NASDAQ chart for today. I don't manually trade it but my stupid computer trades it based on objective logical reasoning and those trades labeled on there are the trades my stupid computer took. Those are the actual entry and exit points it posted on the chart. My computer puts those labels on there not me. Blue lines are profit & red lines are losses. The computer is stupid because it can't think or argue with the charts . . . but it has no emotion either.
The simple answer is: it is impossible to solve a math equation where the elements of that equation are not stable, they are constantly & ever changing? And I agree too . . . it keeps this old man out of trouble as well.
That is also the realm of estimation theory, where you have some rough idea of the dynamics and the noise, and an answer which is "close enough" is good enough. Who cares if you make $100 vs. $110 per contract on a scalp?
In logic and in programming, close enough isn't good enough but I agree with your point. For me it isn't the difference between $100 or $110 per contract, it is the difference between taking a trade or not which is potentially far more expensive.
AFAIAK, noise is high entropy and no order. When you have a trend, you have order. When you have sideways chopping activity, you have noise. Market noise is the result of no specific news, or conflicting news, and information that cannot result in a concrete resolution for price direction for the majority of traders.
We may be closer in attitide than I thought at first. Take the trade, or not? At what downside risk with what entry stop? At what potential loss of upside profit in a reversal while wanting to let it ride to what profit stop? At what loss of further upside profit by taking the statistically correct profit? Within the limits of the typical daily range, you get to pick all those things, given the blessing of an edge.