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AndrewsPitchfork

Incremental, causal technical analysis documentation

Summary

AndrewsPitchfork is RTTA's streaming Andrews Pitchfork built from percent ZigZag-style pivots. Once three alternating pivots are confirmed, each bar emits the median line and parallel upper/lower tines evaluated at the current index, plus pivot and direction flags.

Update API

result = rtta.AndrewsPitchfork(percent_change=0.05, fillna=True).update(high, low, close)
# result.median, result.upper, result.lower, result.pivot, result.direction

percent_change is a fractional threshold (e.g. 0.05 for 5%). Values greater than 1.0 are treated as percent and divided by 100. The first bar seeds state; with fillna=True early outputs use close as a placeholder for all three lines.

Theory Of Operation

Alan Andrews' pitchfork draws a median line from an origin pivot \(P_0\) through the midpoint of the next two pivots \(P_1, P_2\), then places parallel tines offset by the distance of \(P_1\) from that median. Price often reacts near the tines.

RTTA does not take manual pivot coordinates. Instead it discovers pivots online with a percent-change ZigZag on high/low extremes: a high pivot is confirmed when price reverses down by the threshold from the swing high; a low pivot when price reverses up from the swing low. The last three confirmed pivots define the fork; subsequent bars extrapolate the lines using the median slope.

Recurrence

Let \(H_t, L_t, C_t\) be high, low, close and let \(\tau\) be the percent threshold. Maintain swing direction \(d_t \in \{-1,0,+1\}\), extreme price and index, and a ring of up to eight pivots \((p_i, j_i)\) (price and bar index).

Pivot confirmation (ZigZag). Starting from the first close, when \(H_t \ge C_0(1+\tau)\) set direction \(+1\) (upswing); when \(L_t \le C_0(1-\tau)\) set direction \(-1\). During an upswing, track the highest high; confirm a high pivot when \(L_t \le E(1-\tau)\). During a downswing, track the lowest low; confirm a low pivot when \(H_t \ge E(1+\tau)\). Each confirmation pushes \((E, j_E, \pm 1)\) and flips direction. pivot on the result is \(1\) on confirmation bars and \(0\) otherwise.

Pitchfork geometry. When at least three pivots exist, take the last three as \(P_0, P_1, P_2\) (oldest to newest among those three):

\[M^{\text{price}} = \tfrac12(p_1 + p_2), \qquad M^{\text{idx}} = \tfrac12(j_1 + j_2)\]
\[s = \frac{M^{\text{price}} - p_0}{M^{\text{idx}} - j_0} \quad\text{(slope; \(0\) if denominator is zero)}\]

At the current bar index \(t\):

\[\begin{aligned} \operatorname{median}_t &= p_0 + s\,(t - j_0) \\ \delta &= p_1 - \bigl(p_0 + s\,(j_1 - j_0)\bigr) \\ \operatorname{upper}_t &= \operatorname{median}_t + \delta \\ \operatorname{lower}_t &= \operatorname{median}_t - \delta \end{aligned}\]

direction is the live swing direction \(d_t\). Until three pivots exist, fillna=True returns close for all three lines; fillna=False returns NaN.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class AndrewsPitchfork. Result fields are median, upper, lower, pivot, and direction. The pivot buffer holds at most eight pivots (oldest dropped).

Reference