Reconstructing a stochastic oscillator, MACD, and a triple-smoothed oscillator

Rebuild the filter from named pieces

Editorial reading: treat this archive as a swap-one-piece construction drill. Rebuild a stochastic oscillator from a close-in-range ratio, an MACD from two exponential averages and a signal smoother, and a triple-smoothed oscillator from nested exponential updates of the log of price. Then change only the lookback, only the kernel, or only the comparison line, and watch which part of the plotted filter moves.

Percent-K from a close-in-range ratio

A stochastic oscillator is a bounded oscillator that locates the latest close inside a lookback high-low range and then smooths that position onto a 0 to 100 scale. Percent-K, the unsmoothed reading, can be assembled from the latest close, the lowest low over a chosen lookback, and the highest high over that same lookback, then scaled onto a 0 to 100 range.

In the illustrated build, both the highest-high and lowest-low windows use five periods. Those two extrema can be computed as independent series from high, low, and close.

Percent-D is a short-window smoothing of the stochastic numerator and denominator, renormalized to the same 0 to 100 scale. Summing the close-minus-low numerator and the high-minus-low denominator over three periods, then renormalizing, yields percent-D. A three-period simple average of that percent-D yields slow percent-D, a slower companion line.

MACD from two averages and a signal line

MACD is the difference between a shorter and a longer exponential average of closing price, plotted against a signal line. An MACD line can be formed by subtracting a 26-period exponential average of the close from a 12-period exponential average of the close.

The companion signal line is a nine-period exponential average of that MACD difference. The signal line is the comparison series for crosses.

Replacing those exponential averages with simple averages produces a different MACD series. Editorial reading: that replacement is the kernel swap; the subtraction and the signal-line role stay in place.

Nested exponential updates of log price

A triple-smoothed oscillator starts from the log of price, applies three successive exponential updates, and reports 100 times the one-bar change in the third smoother. The three updates share a smoothing alpha equal to 2 divided by the chosen length plus one. Exponential smoothing is a recursive average that updates each bar by blending the newest observation with the prior smoothed value through that fixed weight.

That oscillator can be plotted with a zero line and a linear-regression average. Optional flags can fire on a zero cross, a regression-average cross, or either. A zero cross is true when the centered oscillator moves through the zero reference. A regression-average cross is true when the oscillator moves through a linear-regression average of itself.

Default lengths shown for that construction are 3 for the smoother and 8 for the regression average.

What a one-piece swap changes

Editorial reading: changing the five-period extrema or the three-period sums moves the stochastic lookback and its smoothers. Changing the 12-period average, the 26-period average, or the nine-period signal line, or swapping exponential averages for simple averages, moves the MACD kernel or the comparison series. Changing the shared smoothing alpha or the regression length moves the triple-smoothed oscillator or its comparison line.