QuanTAlib/lib/oscillators/rrsi/Rrsi.md

Rocket RSI (RRSI)

Category: Oscillators Type: Unbounded zero-mean oscillator Author: John F. Ehlers, TASC May 2018

Description

Rocket RSI combines Ehlers' Super Smoother filter with a custom RSI calculation and applies the Fisher Transform to produce a Gaussian-distributed oscillator with sharp turning-point signals ideal for cyclic reversal detection.

Mathematical Foundation

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)

Coefficients (computed once):

a_1 = e^{-1.414\pi / \text{smoothLength}}, \quad b_1 = 2 a_1 \cos(1.414\pi / \text{smoothLength}) c_2 = b_1, \quad c_3 = -a_1^2, \quad c_1 = 1 - c_2 - c_3

Filter:

\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}

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

Parameters

Parameter	Default	Range	Description
smoothLength	10	> 0	Super Smoother filter period
rsiLength	10	> 0	RSI accumulation window

Interpretation

• Values > +2: Overbought — potential sell signal
• Values < −2: Oversold — potential buy signal
• Zero crossings: Momentum shift
• Peaks/troughs: Cyclic turning points

The Fisher Transform produces a nearly Gaussian distribution, meaning:

• ~68% of values fall within ±1 standard deviation
• Values beyond ±2 are statistically extreme (~5%)
• Values beyond ±3 are very rare (~0.3%)

Key Differences from Standard RSI

1. Super Smoother pre-filter removes high-frequency noise
2. Ehlers RSI uses raw summation (not Wilder's exponential smoothing)
3. RSI output is ±1 (not 0–100), already suited for Fisher Transform
4. Fisher Transform converts to Gaussian distribution with sharp reversals

Warmup Period

smoothLength + rsiLength bars are needed for the IIR filter to stabilize and the RSI accumulation window to fill.

C# Usage

// Streaming
var rrsi = new Rrsi(smoothLength: 10, rsiLength: 10);
foreach (var bar in series)
{
    TValue result = rrsi.Update(bar);
    // result.Value is the Rocket RSI
}

// Batch
TSeries results = Rrsi.Batch(series);

// Span
Rrsi.Batch(source, output, smoothLength: 10, rsiLength: 10);

References

• Ehlers, J. F. (2018). "Rocket RSI." Technical Analysis of Stocks & Commodities, May 2018.
• Ehlers, J. F. (2004). Cybernetic Analysis for Stocks and Futures. Wiley.