Stochastic fast and slow construction as a rebuildable stack

This archive note treats a stochastic print as a rebuildable stack before any comparison to a Relative Strength Index band or a dual-period moving-average crossover. The stack is range window, first smooth, second smooth, and label. Editorial framing below separates construction steps from later reading rules.

The raw stochastic, also labeled percent K or Fast K, equals the latest close minus the lowest low over n periods, divided by the highest high minus the lowest low over those n periods, then multiplied by 100. That raw series equals 0 when the close matches the n-period low and 100 when the close matches the n-period high. The lookback n may be any sampling interval that supplies a high, a low, and a close for each bar.

A 3-period moving average of raw percent K is labeled percent D Fast, and a further 3-period average of percent D Fast is labeled percent D Slow. Three constructed series receive four names because percent K Slow is defined as identical to percent D Fast, while percent D Slow is a moving average of that slow percent K.

In a survey of 20 software packages, stochastic smoothing was implemented as a simple, weighted, or exponential moving average, and some packages instead totaled the raw numerator and the raw denominator over a prescribed window. That summed-range path is an alternative slow construction rather than an average of the finished percent K series. A shorter smoothing period is described as marking reversals earlier while admitting more false crossings, and exponentially smoothed averages are presented as a common choice when slow stochastics are built for a short horizon.

One reading rule treats both percent K and percent D above 75 as overbought and below 24 as oversold, in the same manner as a Relative Strength Index overbought or oversold reading. Here the Relative Strength Index supplies only that parallel band convention, not a separate rebuild of its own formula stack.

The same oscillator is also read by comparing its peaks and troughs with price for divergence, or by plotting two periodicities together, including an 8-day and 20-day percent D pair, in the style of moving-average crossovers. The moving average therefore appears twice: as the smoother of raw stochastic values, and as the dual-period crossover template applied to two stochastic lookbacks.

Software labels for fast versus slow and for K versus D are inconsistent across packages. Editorial note: the construction is usable for comparison only when periodicity and smoothing can be changed at each stage, so that a named Fast or Slow line can be rebuilt before it is matched to a band rule or a dual-period plot.