Summary
EhlersDecycler is RTTA's streaming Ehlers decycler. It estimates a
low-frequency decycle component of price (trend-like smooth) and an
oscillator residual \(x_t - \text{decycle}_t\) that emphasizes what was
removed—the higher-frequency content.
Update API
result = rtta.EhlersDecycler(hp_period=60, fillna=True).update(price)
| Parameter | Default | Meaning |
|---|---|---|
hp_period |
60 |
Period controlling the high-pass / decycle cutoff (minimum 2) |
fillna |
True |
If False, NaN until hp_period samples |
update(...) returns:
decycle— low-frequency decycle estimateoscillator— \(price - decycle\)
advance(price) updates state; last() returns the cached result.
Theory Of Operation
Ehlers' decycler is obtained by subtracting a one-pole high-pass from price (equivalently, a complementary low-pass). With high-pass coefficient \(\alpha\) derived from period \(P\), the low-frequency path is:
so \(D_t\) tracks slow structure while the residual \(x_t - D_t\) behaves like a
zero-mean oscillator of faster swings. Larger hp_period pushes more of the
spectrum into the decycle and leaves a quieter oscillator; smaller periods make
the decycle hug price more tightly.
This is simpler than the two-pole roofing filter: a single \(\alpha\) and one lag of price/decycle state.
Recurrence
Let \(P = \max(\texttt{hp\_period}, 2)\):
First sample (\(t = 0\)):
Thereafter:
Result: decycle \(= D_t\), oscillator \(= O_t\).
When fillna=False and fewer than \(P\) samples have been processed, both
fields are NaN.
Implementation Notes
- Implemented in
src/rtta/indicator.cppinclass EhlersDecycler. - Result type:
EhlersDecyclerResult(decycle,oscillator). - State:
price1_,decycle1_, samplecount_. - Note: \(\theta = 2\pi/P\) (no \(0.707\) factor), unlike
EhlersRoofingFilter/ cyber-cycle high-pass. - Batch helper:
batch_ehlers_decycler.