Miha Kralj
e17b00172a
- Eeo.md: full rewrite to canonical template (blockquote, table, 3 bullets, paragraph) - Ac.md: add PineScript row - Ao.md: add PineScript row - Fisher04.md: add table, PineScript row, 3 bullets, paragraph - TtmWave.md: add PineScript row - Dstoch.md: full rewrite header (blockquote, canonical table, 3 bullets, paragraph) - Net.md: add blockquote, canonical table, PineScript row, 3 bullets, paragraph
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EEO: Ehlers Elegant Oscillator
Where DSO shouts through a megaphone, EEO whispers through a compressor — the Inverse Fisher Transform tames extremes into a clean bounded signal.
| Property | Value |
|---|---|
| Category | Oscillator |
| Inputs | Source (close) |
| Parameters | bandEdge (default 20) |
| Outputs | Single series (Eeo) |
| Output range | Bounded ≈ [-1, +1] |
| Warmup | 50 + bandEdge bars |
| PineScript | eeo.pine |
- EEO (Elegant Oscillator) applies the Inverse Fisher Transform (tanh) to RMS-normalized 2-bar momentum, then smooths the result with a 2-pole Super Smoother filter, producing a bounded zero-crossing oscillator.
- Similar: DSO, RSIH | Complementary: ADX for trend confirmation | Trading note: Output bounded ≈ [-1, +1]; ±0.5 levels indicate strong momentum. Unlike DSO (unbounded), EEO compresses extremes via tanh.
- No external validation libraries implement EEO. Validated through self-consistency and behavioral testing.
EEO is Ehlers' 2022 refinement of his earlier DSO (2018). Where DSO applies the Fisher Transform (arctanh) to expand a normalized signal, EEO applies the Inverse Fisher Transform (tanh) to compress it. The IFT naturally bounds the output to [-1, +1] without the ±0.99 clamping that DSO requires. A Super Smoother post-filter then removes residual noise. The fixed 50-bar RMS normalization window provides a stable volatility baseline independent of the BandEdge parameter.
Historical Context
John F. Ehlers published the Elegant Oscillator in the February 2022 issue of Technical Analysis of Stocks & Commodities magazine under the title "An Elegant Oscillator: Inverse Fisher Transform Redux." The article presents EEO as a deliberate counterpart to his 2018 Deviation-Scaled Oscillator (DSO). While DSO uses the Fisher Transform (arctanh) to stretch readings near zero into large excursions, EEO uses the Inverse Fisher Transform (tanh) to compress them — producing a naturally bounded output without the artificial clamping that DSO requires.
Architecture & Physics
Stage 1: 2-Bar Momentum (Derivative)
\text{Deriv} = \text{Close} - \text{Close}[2]
This is the same "zeros" whitening used in DSO — it removes DC and Nyquist components, creating a band-limited derivative.
Stage 2: RMS Normalization (Fixed 50-Bar Window)
\text{RMS} = \sqrt{\frac{1}{50}\sum_{k=0}^{49}\text{Deriv}[k]^2}
\text{NDeriv} = \frac{\text{Deriv}}{\text{RMS}}
The fixed 50-bar window (not parameterized) provides a stable normalization base. The RMS measures the "typical" derivative magnitude, so NDeriv represents "how many standard deviations" the current derivative is from zero.
Stage 3: Inverse Fisher Transform (tanh)
\text{IFish} = \tanh(\text{NDeriv}) = \frac{e^{2 \cdot \text{NDeriv}} - 1}{e^{2 \cdot \text{NDeriv}} + 1}
The IFT compresses the normalized derivative into [-1, +1]. Values near ±1 indicate extreme momentum relative to recent history.
Stage 4: Super Smoother Filter (2-Pole Butterworth)
a_1 = e^{-1.414\pi / \text{BandEdge}}
b_1 = 2 \cdot a_1 \cdot \cos\!\left(\frac{1.414 \cdot 180°}{\text{BandEdge}}\right)
c_2 = b_1, \quad c_3 = -a_1^2, \quad c_1 = 1 - c_2 - c_3
\text{SS} = \frac{c_1}{2}(\text{IFish} + \text{IFish}[1]) + c_2 \cdot \text{SS}[1] + c_3 \cdot \text{SS}[2]
The Super Smoother removes high-frequency chatter from the IFT output while preserving the phase relationship.
Performance Profile
Operation Count (Streaming Mode, Scalar)
| Operation | Count | Notes |
|---|---|---|
| Subtraction (Deriv) | 1 | Close - Close[2] |
| Multiply (deriv²) | 1 | For RMS buffer |
| RingBuffer add/remove | 1 | O(1) circular buffer |
| FMA (running sum) | 1 | SumSq update |
| Sqrt (RMS) | 1 | √(sum/50) |
| Division (normalize) | 1 | Deriv / RMS |
| Exp + tanh (IFT) | 1 | Math.Tanh() |
| FMA × 2 (SSF) | 2 | 2-pole recursive filter |
| Total per bar | ~9 | Constant O(1) |
Batch Mode (SIMD Analysis)
The algorithm's IIR Super Smoother stage prevents full vectorization. Batch mode processes sequentially but avoids per-bar allocation overhead.
Quality Metrics
| Metric | Score | Notes |
|---|---|---|
| Lag | Low | SSF has minimal phase distortion |
| Noise rejection | High | IFT compression + SSF smoothing |
| Sensitivity | High | 2-bar derivative is very responsive |
| Bounded output | Yes | ≈ [-1, +1] from tanh |
| Parameter count | 1 | Only BandEdge |
Validation
EEO is validated through self-consistency tests (streaming ≡ batch ≡ span ≡ eventing) and behavioral tests (constant input → 0, trending → non-zero, symmetry).
Behavioral Test Summary
| Test | Expected Result |
|---|---|
| Constant input | Output → 0 |
| Strong uptrend | Output > 0 |
| Strong downtrend | Output < 0 |
| Ascending vs descending | Opposite signs |
| NaN/Inf input | Finite output (fallback) |
| Bar correction (isNew) | State restored correctly |
Common Pitfalls
-
Fixed RMS window: The 50-bar window is hardcoded per Ehlers' specification. Do not parameterize it — it provides a stable normalization base independent of BandEdge.
-
BandEdge vs Period: BandEdge is the Super Smoother cutoff, not an RMS lookback. Higher BandEdge = more smoothing but more lag.
-
Bounded output: Unlike DSO (which uses Fisher Transform producing unbounded output), EEO output is bounded to ≈ [-1, +1]. Signal levels of ±0.5 are typical thresholds, not ±2 as with DSO.
-
Warmup: Requires 50 + BandEdge bars. The first 50 bars fill the RMS window; then BandEdge more bars are needed for SSF convergence.