EhlersCyberCycle

Summary

EhlersCyberCycle is RTTA's streaming implementation of John Ehlers' cyber-cycle oscillator. Price is lightly smoothed, then a two-pole high-pass extracts the dominant cycle component. A one-bar lag of the cycle is returned as a trigger line for cross-based timing.

Update API

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

Parameter	Default	Meaning
`period`	`20`	High-pass critical period (minimum 2)
`fillna`	`True`	If `False`, NaN until `period` samples

update(...) returns:

cycle — current cyber-cycle value
trigger — previous bar's cycle (one-bar lag used as trigger)

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

Theory Of Operation

The cyber cycle is designed to isolate cyclic content while cancelling trend. RTTA follows Ehlers' practical streaming form:

4-bar weighted smooth of price (once enough history exists): \((x_t + 2x_{t-1} + 2x_{t-2} + x_{t-3})/6\).
Two-pole high-pass of that smooth with coefficient \(\alpha\) from the critical period (same angle construction as the roofing high-pass, \(0.707\cdot 2\pi/P\)).
During a short bootstrap (first 7 samples), a simple second-difference proxy is used so the filter is defined before full recursive state exists.
The trigger is the previous cycle value, so crossings of cycle vs trigger mark short-term cycle turns.

Positive cycle values indicate the cyclic component is above its local zero; negative values indicate the opposite.

Recurrence

Alpha

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

\[\theta = \frac{0.707 \cdot 2\pi}{P},\qquad \alpha = \frac{\cos\theta + \sin\theta - 1}{\cos\theta}\]

Price smooth

For sample index \(t \ge 3\) (zero-based count \(\ge 3\)):

\[s_t = \frac{x_t + 2 x_{t-1} + 2 x_{t-2} + x_{t-3}}{6}\]

Otherwise \(s_t = x_t\).

Cycle bootstrap (\(t < 7\))

\[C_t = \frac{x_t - 2 x_{t-1} + x_{t-2}}{4}\]

Cycle recursion (\(t \ge 7\))

Let \(a = 1 - \alpha/2\):

\[\begin{aligned} C_t &= a^{2}\,(s_t - 2 s_{t-1} + s_{t-2}) \\ &\quad + 2(1-\alpha)\, C_{t-1} \\ &\quad - (1-\alpha)^{2}\, C_{t-2} \end{aligned}\]

Trigger

\[T_t = C_{t-1}\]

(in code, trigger = c1_ is the cycle value before writing the new cycle into state).

Result: cycle \(= C_t\), trigger \(= T_t\).

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 EhlersCyberCycle.
Result type: EhlersCyberCycleResult (cycle, trigger).
Price lags p1_,p2_,p3_; smooth lags s1_,s2_; cycle lags c1_,c2_.
Batch helper: batch_ehlers_cyber_cycle.