A variable-sensitivity stochastic built on three-sigma bounds

A parts swap, not a new study

This is an editorial teaching frame, not an archive claim. A stochastic oscillator is a range-relative reading that locates the latest observation between two bounds computed over a defined lookback, then smooths that reading into successive lines. The usual bounds are a lookback high and low. The construction below swaps those bounds for a three-sigma channel and keeps the rest of the study in the same parts order.

Exponential smoothing is a one-parameter recurrence that blends the previous output with the current observation. In this workflow it is used twice: first as a sensitivity setting on the input series, then as the smoother that forms the slower stochastic lines.

Place the sigma-limits first

Construction starts from finite-lookback sample variance. The square root of that variance is the standard deviation. Sigma-limits are then placed three standard deviations above and below a five-observation average.

A sigma-limit is a bound placed a fixed number of standard deviations above or below a short average of the lookback sample. After those bounds exist, the latest raw observation can be replaced with a smoothed value whose span is about half the lookback. That substitution was used to make the oscillator approach a steadier reading.

Two readings from the same pair of bounds

A top-side statistical oscillator is defined as the latest value's distance above the lower three-sigma bound divided by its distance below the upper three-sigma bound.

A stochastic percent-K analogue uses the last three-sigma pair as the range. It is 100 times the distance from the lower bound to the latest value, divided by the full distance between the two bounds. The next two stochastic lines are successive exponential smooths of that percent-K reading. Each uses a coefficient of 0.35, chosen by experiment.

Sensitivity is a pre-smoothing coefficient

Sensitivity is the pre-smoothing coefficient applied to the input series before variance, channel, and oscillator calculations. The series is exponentially smoothed first, using the previous output plus alpha times the gap to the current observation. Alpha was described as useful from 0.05 to 1.0.

A fast meter or a flattening band

Editorial reading: once the range has been swapped, the same sensitivity setting chooses how the study behaves. On short lookbacks with moderate pre-smoothing near 0.08, the smoothed stochastic lines were observed to flatten near 70 percent or 30 percent while a trend persisted. Windows of five or six days were described as best for that flattening.

Raising the pre-smoothing coefficient to 0.10 or higher was described as increasing reactions to minor pinches rather than only larger contractions. Editorial reading: a lower sensitivity setting favors the flattening band, while a higher setting makes the study react more like a fast crossing meter.

The same bounds as a price channel

A price channel, in this construction, is a pair of moving statistical bounds around a smoothed series that stay roughly parallel in a trend and contract when variation pinches. Plotted around the pre-smoothed series, the same three-sigma bounds act as that moving channel. They stay roughly parallel in a trend and pinch when variation contracts around a larger directional move.