> *Rocket RSI strips noisy momentum down to its cyclic core, then Fisher-transforms it into a Gaussian — because reversals should announce themselves with a bang, not a whisper.*
- Ehlers' Rocket RSI chains three transformations — momentum extraction, Super Smoother filtering, and Fisher Transform — to produce a Gaussian-distributed oscillator with sharp turning-point signals.
- Validated against manual step-by-step reference implementation of the original TASC algorithm.
Rocket RSI solves a fundamental problem with conventional RSI: the bounded [0, 100] output compresses extreme readings into a narrow band, making precise reversal timing ambiguous. By applying the Fisher Transform (arctanh) to a summation-based RSI computed on Super-Smoothed momentum, Rocket RSI produces sharp Gaussian peaks at cyclic turning points. The Super Smoother pre-filter removes aliasing artifacts that corrupt cycle analysis, while the Fisher Transform stretches values near ±1 toward ±∞, creating unambiguous inflection points.
## Historical Context
John Ehlers published Rocket RSI in the May 2018 issue of *Technical Analysis of Stocks & Commodities* magazine. The indicator represents the intersection of three areas Ehlers had refined over two decades: the Super Smoother filter (introduced in *Cybernetic Analysis for Stocks and Futures*, 2004), summation-based RSI (a departure from Wilder's exponential smoothing), and the Fisher Transform (first presented in his November 2002 TASC article). By combining these three techniques into a single pipeline, Ehlers created an oscillator specifically designed for cyclic reversal detection rather than trend-following.
The key insight was that conventional RSI, computed on raw price data, conflates cyclic and trend components. The Super Smoother acts as a low-pass filter that isolates the dominant cycle, and the summation-based RSI provides a signed measure of directional pressure without the lag introduced by Wilder's exponential decay. The Fisher Transform then converts this into a Gaussian distribution where standard deviation has statistical meaning.
## Architecture & Physics
### 1. Momentum Extraction
[`Update()`](Rrsi.cs:107) computes half-cycle momentum as `Close[i] - Close[i - rsiLength + 1]` using a [`RingBuffer`](Rrsi.cs:36) of size `rsiLength` for O(1) lookback access. This captures the price change over approximately one half-cycle of the dominant period.
### 2. Super Smoother Filter (2-Pole Butterworth IIR)
The momentum is smoothed by a 2-pole Butterworth low-pass filter with coefficients computed once in the [constructor](Rrsi.cs:82): `a1 = exp(-1.414π / smoothLength)`. The filter equation uses `(Mom + Mom[prev]) / 2` as input (simple averaging of adjacent momentum values), which provides an additional anti-aliasing effect. The filter history is stored in the [`_filtBuf`](Rrsi.cs:39) RingBuffer for RSI accumulation.
### 3. Ehlers RSI (Summation-Based)
Unlike Wilder's RSI which uses exponential moving averages of gains and losses, Ehlers RSI sums raw up-changes (CU) and down-changes (CD) of the filtered value over the last `rsiLength` bars, then computes `(CU - CD) / (CU + CD)`. This produces a value in [-1, +1] without the asymmetric decay that causes Wilder's RSI to understate momentum reversals.
### 4. Fisher Transform
The RSI value is clamped to ±0.999 (preventing log domain errors) and passed through `arctanh(x) = 0.5 × ln((1 + x) / (1 - x))`. This nonlinear stretching converts the near-uniform RSI distribution into a Gaussian, amplifying values near the extremes where reversals occur.
### 5. State Management
The [`State`](Rrsi.cs:42) record struct holds momentum history, filter state, and bar count. The `_s`/`_ps` pattern enables bar correction: when `isNew = false`, the previous state (`_ps`) is restored before recalculating, ensuring that intra-bar updates do not corrupt the indicator state.
### 6. Edge Cases
- **NaN/Infinity inputs**: [Last-valid substitution](Rrsi.cs:112); falls back to 0.0 if no valid data has been seen.
- **Insufficient history**: Momentum defaults to 0.0 when the close buffer has fewer than `rsiLength` entries; filter passes momentum through directly for the first two bars.
- **Zero denominator**: When CU + CD < 1e-10 (no price movement), RSI defaults to 0.0.
- The unbounded nature means threshold levels should be calibrated per instrument and timeframe. What constitutes "extreme" for a low-volatility bond ETF differs from a crypto pair.
- Rocket RSI is designed for **cyclic markets**. In strongly trending markets, the oscillator can remain at extreme values for extended periods. Do not fade a trend solely because Rocket RSI appears overbought.
- Both `smoothLength` and `rsiLength` control the effective cycle period. Increasing either parameter makes the indicator more selective (fewer but higher-quality signals) at the cost of lag.
- Unlike Wilder's RSI (0–100), Rocket RSI is centered at zero and unbounded. There is no direct mapping between RSI levels (e.g., 70/30) and Rocket RSI values.
## Related Indicators
- [**Fisher Transform**](../fisher/Fisher.md): Same arctanh step, but applied to min/max-normalized price rather than RSI.
- [**RSI**](../../momentum/rsi/Rsi.md): Wilder's original bounded [0, 100] momentum oscillator.
- [**RSX**](../../momentum/rsx/Rsx.md): Jurik's ultra-smooth RSI variant using cascaded IIR filters.
- [**StochRSI**](../stochrsi/Stochrsi.md): Stochastic applied to RSI output, another approach to sharpening RSI signals.
## Validation
No external C# library implements Rocket RSI. Validation is performed against a manual step-by-step reference implementation of the original Ehlers TASC May 2018 algorithm.
### Internal Consistency
| Check | Status | Notes |
|-------|--------|-------|
| Manual computation cross-check | ✅ | Batch output matches step-by-step ManualRocketRsi() within 1e-9 for 10,000 points |
1.**Treating Rocket RSI as bounded.** Unlike Wilder's RSI [0, 100], Rocket RSI output has no fixed upper/lower limit. The ±0.999 clamp limits the theoretical maximum to about ±3.8, but there are no "overbought/oversold lines" that work universally.
2.**Confusing with Wilder's RSI.** Rocket RSI uses summation-based CU/CD (not exponential decay), inputs are Super-Smoothed momentum (not raw price), and the output passes through arctanh. The only shared concept is "relative strength."
3.**Using in trending markets.** Rocket RSI is optimized for cyclic reversals. In strong trends, it can remain at extreme values for many bars. Fading a trend based on Rocket RSI alone is a common source of losses.
4.**Ignoring the warmup.** The first `smoothLength + rsiLength` bars produce unreliable output as the IIR filter and RSI accumulation window are not yet fully populated.
5.**Over-parameterizing.** Both `smoothLength` and `rsiLength` affect the effective cycle period. Changing both simultaneously makes it difficult to attribute signal changes. Adjust one parameter at a time.
## FAQ
**Q: Why is the output unbounded while RSI is bounded?**
A: The Fisher Transform (arctanh) maps (-1, 1) to (-∞, +∞). This is intentional: it amplifies the distinction between "at the extreme of the RSI range" and "moderately positioned," producing sharper reversal signals. The ±0.999 clamp limits the theoretical maximum to about ±3.8.
**Q: Why use summation-based RSI instead of Wilder's?**
A: Wilder's exponential decay gives disproportionate weight to recent changes, which can mask cyclic turning points. Ehlers' summation approach treats all changes within the window equally, providing a cleaner measure of directional pressure over exactly one cycle period.
**Q: How does the Super Smoother differ from a simple moving average?**
A: The Super Smoother is a 2-pole Butterworth IIR filter with unity DC gain. Unlike an SMA, it has a steep frequency rolloff that effectively removes aliasing artifacts above the Nyquist frequency of the sampled cycle. This prevents high-frequency noise from corrupting the RSI calculation.
**Q: What values indicate a reversal?**
A: Values beyond ±2.0 indicate statistically extreme readings (~5% of a Gaussian distribution). Sharp peaks followed by zero-line crosses provide the highest-confidence reversal signals. The exact threshold depends on the instrument's volatility characteristics.
