Constructing a double-smoothed stochastic oscillator

A bounded close-in-range reading

The stochastic oscillator is a bounded 0-100 reading of where the close sits between a lookback high and a lookback low. The raw stochastic is one hundred times the close minus the lookback low, divided by the lookback high minus the lookback low, and is scaled onto a zero-to-one-hundred range.

A popular companion line sums the same numerator and denominator over three intervals after a five-interval high-low window, rather than only averaging the already-normalized raw value.

Why extra smoothing is added later

Extra smoothing is motivated by the unsmoothed oscillator revealing many minor swings when only selected peaks and troughs are wanted.

Editorial: that motive is a reason to keep smoothness as later construction choices. It is not a reason to replace the high-low window with one longer preset length.

Two exponential passes on each side of the ratio

The double-smoothed stochastic is the same range-normalized ratio after two successive exponential averages are applied separately to the numerator and the denominator.

The double-smoothed form applies a y-length exponential average and then a z-length exponential average to both the close-minus-lookback-low series and the lookback-high-minus-lookback-low series before multiplying the ratio by one hundred.

Editorial: rebuild the oscillator in that order. Choose the high-low window first, then the first exponential pass, then the second exponential pass, so smoothness can be added without collapsing those choices into a single preset length.

From length to smoothing constant

Exponential smoothing is a recursive average that blends the latest observation with the prior average using a constant estimated as two divided by length plus one.

The exponential length y maps to a smoothing constant of two divided by y plus one. A length of two equals a constant of two-thirds, and a length of one omits that averaging pass.

An exponential average is updated as the prior average plus the smoothing constant times the gap between the new observation and that prior average, equivalently alpha times the new observation plus one minus alpha times the prior average.

Companion averages

A moving average is an arithmetic average of recent values, used both inside the classic companion line and as a slower overlay on the finished double-smoothed oscillator.

A slower companion is formed by taking a three-day arithmetic moving average of the finished double-smoothed oscillator.

The one-bar HLC index

Setting the high-low window to one bar locates the close inside that bar's range and then applies the two exponential passes, producing a faster-responding close-in-range variant.

That one-bar lookback case is the HLC index: it locates the close inside that bar's high-low range before the two exponential passes.

Documented parameter triples

Documented parameter triples include a two-bar window with three-then-fifteen-day exponential passes, a one-bar window with five-then-fifteen-day exponential passes, and a five-bar window with seven-then-three-day exponential passes.

Editorial: the triples show different pairings of the high-low window with the two exponential lengths. They are construction examples, not a ranking.