Ichimoku - RTTA

Summary

Ichimoku is a streaming Ichimoku Kinko Hyo component set: conversion line (Tenkan-sen), base line (Kijun-sen), leading Span A and Span B (undelayed causal values), Chikou / lagging span, and cloud spans delayed by window2 so they align with the bar where the cloud is traditionally plotted (span_a_displaced, span_b_displaced).

Update API

import rtta

ind = rtta.Ichimoku(window1=9, window2=26, window3=52, fillna=True)
result = ind.update(high, low, close)
# result.conversion, result.base, result.span_a, result.span_b,
# result.lagging_span,
# result.span_a_displaced, result.span_b_displaced

advance(...) updates state without returning a result. Batch returns parallel arrays for all seven fields.

Theory Of Operation

Ichimoku uses midpoints of rolling high–low ranges:

Component	Classic name	Definition
conversion	Tenkan-sen	midpoint of high/low over `window1`
base	Kijun-sen	midpoint over `window2`
span_a	Senkou Span A (raw)	midpoint of conversion and base
span_b	Senkou Span B (raw)	midpoint of high/low over `window3`
lagging_span	Chikou Span	close delayed by `window2`
span_a_displaced	cloud A at “now”	raw span_a delayed by `window2`
span_b_displaced	cloud B at “now”	raw span_b delayed by `window2`

In classical charts, Senkou spans are plotted forward by 26 bars. In a causal stream you cannot emit future values, so RTTA also emits the spans that arrive on the current bar: the values computed window2 steps ago. The undelayed span_a / span_b remain available for custom leading-cloud logic.

With fillna=False, incomplete range windows yield NaN for that component. Delay lines use the same fillna policy; NaN raw spans are replaced by close when filling so the delay buffer stays defined.

Recurrence

Let \(n_1,n_2,n_3\) be window1, window2, window3. Rolling extremes over the last \(n\) highs/lows:

\[\begin{aligned} C_t &= \tfrac12\bigl(\max_{i\in[t-n_1+1,t]} H_i + \min_{i\in[t-n_1+1,t]} L_i\bigr),\\ B_t &= \tfrac12\bigl(\max_{i\in[t-n_2+1,t]} H_i + \min_{i\in[t-n_2+1,t]} L_i\bigr),\\ A_t &= \tfrac12(C_t + B_t),\\ S_t &= \tfrac12\bigl(\max_{i\in[t-n_3+1,t]} H_i + \min_{i\in[t-n_3+1,t]} L_i\bigr). \end{aligned}\]

Lagging (Chikou) and displaced cloud (delays of length \(n_2\)):

\[\mathrm{lagging\_span}_t = c_{t-n_2} \quad\text{(Delay of close; NaN until the delay is full if `fillna=False`)},\]

\[\begin{aligned} A^{\mathrm{in}}_t &= \begin{cases} A_t, & A_t \text{ finite},\\ c_t, & \text{NaN and `fillna`}\\ \text{NaN}, & \text{NaN and not `fillna`}, \end{cases} \qquad \mathrm{span\_a\_displaced}_t = A^{\mathrm{in}}_{t-n_2}, \end{aligned}\]

and likewise for \(S_t \rightarrow \mathrm{span\_b\_displaced}_t\).

Public fields: conversion\(= C_t\), base\(= B_t\), span_a\(= A_t\), span_b\(= S_t\).

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class Ichimoku using RollingExtreme for highs/lows and Delay for lagging and displaced spans. Result type is IchimokuResult / IchimokuBatchResult.

Reference

Investopedia — Ichimoku Cloud