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RRSI: Ehlers Rocket RSI

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.

Property Value
Category Oscillator
Inputs Source (close)
Parameters smoothLength (default 10), rsiLength (default 10)
Outputs Single series (RocketRSI)
Output range Unbounded (typically -4 to +4)
Warmup smoothLength + rsiLength bars
PineScript rrsi.pine
  • 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.
  • Similar: Fisher, StochRSI | Complementary: Bollinger Bands for volatility context | Trading note: Unbounded oscillator; values beyond ±2 indicate statistical extremes. Not Wilder's RSI — uses Ehlers summation-based RSI variant.
  • 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() computes half-cycle momentum as Close[i] - Close[i - rsiLength + 1] using a RingBuffer 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: 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 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 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; 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.

Mathematical Foundation

Core Formula

Step 1 — Half-Cycle Momentum:

$$\text{Mom}_i = \text{Close}_i - \text{Close}_{i - (\text{rsiLength} - 1)}$$

Step 2 — Super Smoother Filter (2-pole Butterworth IIR):

Coefficients (computed once):

$$a_1 = e^{-1.414\pi / \text{smoothLength}}, \quad b_1 = 2 a_1 \cos!\left(\frac{1.414\pi}{\text{smoothLength}}\right)$$

$$c_2 = b_1, \quad c_3 = -a_1^2, \quad c_1 = 1 - c_2 - c_3$$

Filter recursion:

$$\text{Filt}_i = c_1 \cdot \frac{\text{Mom}_i + \text{Mom}_{i-1}}{2} + c_2 \cdot \text{Filt}_{i-1} + c_3 \cdot \text{Filt}_{i-2}$$

The DC gain constraint $c_1 + c_2 + c_3 = 1$ ensures the filter passes constant signals without attenuation.

Step 3 — Ehlers RSI (normalized to ±1):

Over the last rsiLength bars of filter differences:

$$CU = \sum_{j=0}^{n-1} \max(\text{Filt}_{i-j} - \text{Filt}_{i-j-1},\ 0)$$

$$CD = \sum_{j=0}^{n-1} \max(\text{Filt}_{i-j-1} - \text{Filt}_{i-j},\ 0)$$

$$\text{RSI} = \frac{CU - CD}{CU + CD} \in [-1, 1]$$

Step 4 — Fisher Transform:

$$\text{RocketRSI} = \text{arctanh}!\left(\text{clamp}(\text{RSI}, \pm0.999)\right) = \frac{1}{2} \ln!\left(\frac{1 + v}{1 - v}\right)$$

Parameter Mapping

Parameter Formula role Default Constraint
smoothLength Cutoff period for the Super Smoother low-pass filter 10 > 0
rsiLength Summation window for CU/CD accumulation and momentum lookback 10 > 0

Warmup Period

$$W = \text{smoothLength} + \text{rsiLength}$$

Default configuration (10, 10) warms up in 20 bars.

Interpretation and Signals

Signal Zones

Zone Rocket RSI value Meaning
Strong overbought > +2.0 Extreme bullish stretch, reversal probable
Overbought +1.0 to +2.0 Bullish momentum, watch for exhaustion
Neutral -1.0 to +1.0 No directional conviction
Oversold -2.0 to -1.0 Bearish momentum, watch for recovery
Strong oversold < -2.0 Extreme bearish stretch, reversal probable

Signal Patterns

  • Zero-line cross: Rocket RSI crossing zero indicates a shift in momentum direction; the Super Smoother removes false crossings from noise.
  • Reversal from extreme: Sharp peak above +2.0 followed by downturn warns of impending sell-off; mirror for buy signals below -2.0.
  • Divergence: Price making new highs with Rocket RSI making lower highs signals cycle exhaustion.
  • Peak sharpness: The Fisher Transform creates V-shaped peaks rather than rounded tops, making the exact bar of reversal unambiguous.

Practical Notes

  • 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: Same arctanh step, but applied to min/max-normalized price rather than RSI.
  • RSI: Wilder's original bounded [0, 100] momentum oscillator.
  • RSX: Jurik's ultra-smooth RSI variant using cascaded IIR filters.
  • StochRSI: 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
Multiple parameter combos ✅ Validated across (5,5), (8,10), (10,10), (10,20), (20,10)
arctanh identity ✅ 0.5 × ln((1+v)/(1-v)) matches Math.Atanh(v) within 1e-12
Super Smoother DC gain ✅ c1 + c2 + c3 = 1.0 verified within 1e-12 for periods 5, 8, 10, 20, 50
Streaming vs Batch vs Span ✅ All three modes agree within 1e-9
Event-based vs Streaming ✅ Identical within 1e-12
All outputs finite ✅ Verified for periods (5,5), (10,10), (20,20), (50,10) across 10,000 bars

Performance Profile

Key Optimizations

  • Precomputed IIR coefficients: c1, c2, c3 calculated once in constructor, avoiding repeated transcendental calls.
  • RingBuffer for O(1) access: Both close history and filter history use RingBuffers; Add and UpdateNewest are constant-time.
  • ArrayPool in Batch: Span-based batch uses ArrayPool<double>.Shared to avoid heap allocation for temporary arrays.
  • State copy pattern: _s/_ps record struct enables bar correction without allocation.
  • [SkipLocalsInit]: Eliminates zero-initialization overhead for stack locals.
  • [MethodImpl(AggressiveInlining)]: Hot-path methods are inlined by the JIT.

Operation Count (Streaming Mode)

Operation Count per bar
Additions ~rsiLength + 4 (RSI summation + filter + momentum)
Multiplications 3 (filter: c1, c2, c3)
Comparisons rsiLength (CU/CD classification)
Log 1 (arctanh)
Division 1 (RSI ratio)
Clamp 1

SIMD Analysis (Batch Mode)

Aspect Status
Momentum computation Scalar (lookback dependency)
Super Smoother filter Scalar (IIR recursion, sequential dependency)
RSI summation Scalar (forward-looking accumulation per bar)
Fisher Transform Scalar (Math.Log, not vectorizable)
Vectorization potential Low — IIR chain + logarithm prevents SIMD

Common Pitfalls

  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.

References

  • Ehlers, John F. "Rocket RSI." Technical Analysis of Stocks & Commodities, May 2018.
  • Ehlers, John F. Cybernetic Analysis for Stocks and Futures. Wiley, 2004.
  • Ehlers, John F. "Using The Fisher Transform." Stocks & Commodities, November 2002.
  • PineScript reference