Use profit mapping to keep a cycle and stop plateau

The historically richest pair is not the test

Searching every combination of two rule parameters for the single historically highest profit is treated as fitting the model to back data. That search is not, by itself, evidence that those parameters will remain useful after market characteristics change.

In this workflow that exhaustive search is system optimization. It is treated as curve-fitting unless it is replaced by a low-sensitivity region.

Read the map by slope as well as height

Profit mapping is a grid of historical system results over two independent rule parameters, plotted so profit is height and each pair can be judged by slope as well as height. A three-dimensional map with one parameter on each horizontal axis and profit as height is used to locate a region where small moves in both parameters leave profit nearly unchanged.

Parameter sensitivity is how sharply mapped profit changes when either rule parameter is moved a small step away from a candidate pair. A parameter plateau is a region of the profit surface where results stay acceptable while both parameters vary, and that region is preferred over an isolated peak.

Low-sensitivity regions on that map are often distant from the parameter pair that produced the single highest historical profit. Robustness testing judges a parameter pair by whether profit stays stable under parameter steps, added noise, and a longer sample window.

Systems that already have two parameters

Two-average crossovers, triple averages with two legs held in a fixed ratio, stochastics, relative-strength index, and parabolic stop-and-reverse are presented as systems that already have two parameters or can be rewritten so the same mapping applies.

Axes for a cycle-timed entry and an accelerating stop

For a cycle-timed entry paired with an accelerating stop, the mapped axes are dominant-cycle length and initial stop offset. The dominant cycle is the measured periodic length used as one independent input to a cycle-timed entry and as the lookback that scales the initial stop.

Initial stop offset is a multiplier, allowed to range from 0.25 to 2.5, applied to average daily range over the most recent half cycle to set the first stop distance from the entry-day price extreme.

A clean theoretical cycle formed a ridge

On a noise-free theoretical 20-day cycle spanning 80 days, profit formed a ridge centered on a 20-day dominant cycle and showed no material sensitivity to the offset parameter. Overestimating cycle length reduced profit less than underestimating it.

Noise can turn a peak into a cliff

Noise at one-fourth the sine-wave amplitude left the profitable parameter region largely unchanged. Noise equal to the sine-wave amplitude kept the peak at a 20-day cycle only at the largest offset, and that peak sat beside a steep drop into losses.

Signal-to-noise ratio is the relative strength of the cyclic component versus additive noise. When parameter sensitivity is high because the signal-to-noise ratio is poor, the mapping procedure treats the surface as a reason not to trade rather than a reason to take the peak. When that ratio is poor the surface becomes too peaked to justify selecting any pair.

A longer window is used to check the plateau

A two-month pork-bellies map placed the historically richest pair at a 32-day dominant cycle and a 0.25 offset on a steep drop, while a 12-day cycle with a 0.5 offset sat in the center of a broader mound. A full-year map of the same contract kept that two-month plateau pair inside a still-consistent profitable-parameter region.