EhlersInstantaneousTrendline

Summary

EhlersInstantaneousTrendline is RTTA's streaming Ehlers instantaneous trendline: a two-pole recursive smoother with a four-sample input average and a two-bar extrapolated trigger line for timing.

Update API

result = rtta.EhlersInstantaneousTrendline(period=20, fillna=True).update(price)

Parameter	Default	Meaning
`period`	`20`	Critical period \(P\) (minimum 2)
`fillna`	`True`	If `False`, NaN until `period` samples

update(...) returns:

trendline — instantaneous trendline
trigger — \(2\cdot\text{trendline}_t - \text{trendline}_{t-2}\)

advance(price) updates state; last() returns the cached result.

Theory Of Operation

Ehlers' instantaneous trendline is a low-lag smooth of price intended to track the local mean of the cycle component without waiting for a long moving-average window. Coefficients match the Super Smoother pole placement (\(\sqrt{2}\,\pi / P\)), but the feed-forward gain is distributed as \(c_1 = (1-c_2-c_3)/4\) over a three-term average of price \((x_t + 2x_{t-1} + x_{t-2})\), which is the discrete form used in Ehlers' iTrend presentations.

The trigger is a two-bar linear extrapolation of the trendline (\(2 y_t - y_{t-2}\)). Crosses of trendline and trigger mark short-term turns of the smooth, analogous to a signal line without an extra EMA.

This indicator is distinct from TA-Lib / RTTA HilbertTrendline, which adapts the averaging length from a Hilbert dominant-cycle estimate rather than a fixed period.

Recurrence

Let \(P = \max(\texttt{period}, 2)\). Precompute:

\[\theta = \frac{\sqrt{2}\,\pi}{P},\qquad a_1 = e^{-\theta},\qquad b_1 = 2 a_1 \cos(\theta)\]

\[c_2 = b_1,\qquad c_3 = -a_1^{2},\qquad c_1 = \frac{1 - c_2 - c_3}{4}\]

For the first two samples:

\[I_t = x_t\]

Thereafter:

\[I_t = c_1\,(x_t + 2 x_{t-1} + x_{t-2}) + c_2\, I_{t-1} + c_3\, I_{t-2}\]

Trigger (using trend state before shifting; after update, \(t2\) is the prior prior trend):

\[Trig_t = 2 I_t - I_{t-2}\]

In code: trigger = 2.0 * trend - t2_ where t2_ is still the old two-bar-ago trendline at computation time, then state shifts t2_ ← t1_ ← trend.

Result: trendline \(= I_t\), trigger \(= Trig_t\).

When fillna=False and fewer than \(P\) samples have been processed, both fields are NaN.

Implementation Notes

Implemented in src/rtta/indicator.cpp in class EhlersInstantaneousTrendline.
Result type: EhlersInstantaneousTrendlineResult (trendline, trigger).
Price lags p1_,p2_; trend lags t1_,t2_.
Batch helper: batch_ehlers_itrend.

Summary

Update API

Theory Of Operation

Recurrence

Implementation Notes

Reference