Function specialK

Pring's Special K (Martin Pring) — the kst construction extended from four terms to twelve, so that one line carries the short-, intermediate- and long-term momentum of the whole business cycle at once:

term_i    = SMA(ROC(column, roc_i), smooth_i)     ROC in PERCENT
${output} = Σ weight_i · term_i

  group        short-term            intermediate            long-term
  roc_i      10   15   20   30     40   65   75  100     195  265  390  530
  smooth_i   10   10   10   15     50   65   75  100     130  130  130  195
  weight_i    1    2    3    4      1    2    3    4       1    2    3    4
Copy

Appends one column, in percent-times-weight units (the weights sum to 30). Pring's claim for it is that the primary trend turns — the ones a four-term KST is too fast to call — show up as the Special K's own peaks and troughs, so it is read as a primary-trend indicator rather than as a trading oscillator.

It composes on the same two primitives kst does — percentChangeValues for each rate of change and rollingMeanValues for each smoothing — so the two studies share one definition of both, and the only difference between them is the table above.

The thirty-six numbers are the study — there are no options

column and output are the whole option list, and that is the same decision kst records: Pring published several Special Ks (this daily set, and weekly and monthly ones), and they are different indicators with different readings rather than one indicator with parameters. Arrays of periods on this function would make specialK() name all of them at once. Unlike kst, there is not even a signalPeriod: Pring's Special K is read against its own moving average when a signal is wanted, and that is sma() over the output column — a shipped primitive, not a second column this study has to name.

The warm-up is 724 bars — read this before pointing it at a chart

The slowest term is a 530-bar rate of change smoothed over 195 bars, so the line first exists at bar 530 + 195 − 1 = 724 and a series needs 725 bars to produce a single value. That is not a defect: Pring's design deliberately reaches back about three years of daily data so that the long group can see a whole cycle. A study run on a year of bars comes back entirely undefined, with the row count preserved.

The line is defined exactly where all twelve terms are, with no branch in the code — a missing term is NaN and survives the addition.

Definition, verified

No TA-Lib function. The oracle is a pandas replication over a longer input than the rest of the fixture uses (900 bars, generated the same deterministic way), with the analytic first-valid bar (724) asserted and two discriminating separations measured — 156.73 from an equal-weight sum and 281.23 from a sum of unsmoothed rates of change, on a line spanning −260.73 … 159.45. Both survive the shape of the study, which is why they are the probes.

The long input exists because of this study: a 530-bar look-back cannot warm up inside the 80-bar fixture, and a case that came back entirely undefined would pass vacuously. It carries a much slighter drift than the short one, because a steadily rising series makes all twelve rates of change positive at once and the line never crosses zero (measured: 151.5 … 379.3 at the first drift tried).

The rates of change are percent ((x/x[−n] − 1)·100), matching percentChange and TA-Lib's ROC; a ratio form would shift each term by 100 and the whole line by 3000.

Edges

• Scale-invariant, not shift-invariant — every term is a ratio, so multiplying every price leaves the line alone while adding a constant changes each ratio. The same pair kst has, and pinned the same way.
• A zero look-back base → undefined for that term, and the sum with it, inherited from percentChangeValues. Unreachable on prices.
• An interior gap blanks the bar, the twelve bars that read it as a look-back base, and every smoothing window holding one of those — then recovers. With smoothings up to 195 bars that is a wide hole, but it is a hole and not a tail: no recursion is involved.