Constant false-alarm rate for dominant-cycle stops

Four outcomes of a yes-or-no decision

A detection-style yes-or-no decision at each step has four outcomes: correct acceptance, correct rejection, a false alarm, and a missed detection. A false alarm is a yes-vote that treats noise as if a usable signal were present. A missed detection is a no-vote that fails to register a signal that was actually present.

Under the value function used here, a missed detection is treated as a nearly costless skipped opportunity, while a false alarm is assigned a large negative value.

A constant false-alarm rate

A sequential observer updates its threshold from experience to hold a roughly constant false-alarm rate. That policy is offered as the basis for an adaptive rule: hold the rate of incorrect yes-votes near a chosen level instead of maximizing detections.

How the trailing reverse order ages

The demonstration entry-exit rule is a stop-and-reverse order whose initial placement is fixed. The trailing-stop then accelerates in proportion to the age of the open trade relative to an assumed dominant cycle. The dominant cycle is the cycle length assumed by the stop-acceleration rule. It scales how quickly the trailing reverse order closes the gap as a trade ages.

The stop update adds a share of the previous gap to the prior stop. That share grows with trade age relative to the assumed dominant cycle.

If the assumed cycle is too long, the reverse order lags and captured excursion shrinks. If it is too short, the order tightens too fast and produces whipsaw reversals.

Scan the parameter or stand aside

With no known cycle period, the stop-acceleration parameter is scanned across candidate dominant-cycle lengths. System optimization is that scan of one rule parameter over a recent window. It selects the value that keeps incorrect yes-votes at an acceptable rate, or refuses the trade if no such value appears. Winners are tallied as detections and losers as false alarms.

The controlled price path is a sine wave. A noisier variant of the same path is used as well. The scan is described as associating the highest plotted results with a low but finite false-alarm count rather than driving false alarms to zero.

When no clear constant-false-alarm-rate parameter appears, the procedure treats that outcome as a stand-aside signal because the span may be too noisy or the rule may not fit.