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88 lines
2.9 KiB
Markdown
88 lines
2.9 KiB
Markdown
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# Rocket RSI (RRSI)
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**Category:** Oscillators
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**Type:** Unbounded zero-mean oscillator
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**Author:** John F. Ehlers, TASC May 2018
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## Description
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Rocket RSI combines Ehlers' Super Smoother filter with a custom RSI calculation
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and applies the Fisher Transform to produce a Gaussian-distributed oscillator
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with sharp turning-point signals ideal for cyclic reversal detection.
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## Mathematical Foundation
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### Step 1: Half-Cycle Momentum
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$$\text{Mom}_i = \text{Close}_i - \text{Close}_{i - (\text{rsiLength} - 1)}$$
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### Step 2: Super Smoother Filter (2-Pole Butterworth)
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Coefficients (computed once):
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$$a_1 = e^{-1.414\pi / \text{smoothLength}}, \quad b_1 = 2 a_1 \cos(1.414\pi / \text{smoothLength})$$
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$$c_2 = b_1, \quad c_3 = -a_1^2, \quad c_1 = 1 - c_2 - c_3$$
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Filter:
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$$\text{Filt}_i = c_1 \cdot \frac{\text{Mom}_i + \text{Mom}_{i-1}}{2} + c_2 \cdot \text{Filt}_{i-1} + c_3 \cdot \text{Filt}_{i-2}$$
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### Step 3: Ehlers RSI (Normalized to ±1)
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Over the last `rsiLength` bars of filter differences:
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$$CU = \sum_{j=0}^{n-1} \max(\text{Filt}_{i-j} - \text{Filt}_{i-j-1},\ 0)$$
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$$CD = \sum_{j=0}^{n-1} \max(\text{Filt}_{i-j-1} - \text{Filt}_{i-j},\ 0)$$
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$$\text{RSI} = \frac{CU - CD}{CU + CD} \in [-1, 1]$$
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### Step 4: Fisher Transform
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$$\text{RocketRSI} = \frac{1}{2} \ln\left(\frac{1 + \text{clamp(RSI, \pm0.999)}}{1 - \text{clamp(RSI, \pm0.999)}}\right) = \text{arctanh}(\text{RSI})$$
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## Parameters
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| Parameter | Default | Range | Description |
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|-----------|---------|-------|-------------|
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| smoothLength | 10 | > 0 | Super Smoother filter period |
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| rsiLength | 10 | > 0 | RSI accumulation window |
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## Interpretation
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- **Values > +2**: Overbought — potential sell signal
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- **Values < −2**: Oversold — potential buy signal
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- **Zero crossings**: Momentum shift
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- **Peaks/troughs**: Cyclic turning points
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The Fisher Transform produces a nearly Gaussian distribution, meaning:
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- ~68% of values fall within ±1 standard deviation
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- Values beyond ±2 are statistically extreme (~5%)
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- Values beyond ±3 are very rare (~0.3%)
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## Key Differences from Standard RSI
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1. **Super Smoother pre-filter** removes high-frequency noise
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2. **Ehlers RSI** uses raw summation (not Wilder's exponential smoothing)
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3. **RSI output is ±1** (not 0–100), already suited for Fisher Transform
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4. **Fisher Transform** converts to Gaussian distribution with sharp reversals
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## Warmup Period
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`smoothLength + rsiLength` bars are needed for the IIR filter to stabilize
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and the RSI accumulation window to fill.
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## C# Usage
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```csharp
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// Streaming
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var rrsi = new Rrsi(smoothLength: 10, rsiLength: 10);
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foreach (var bar in series)
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{
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TValue result = rrsi.Update(bar);
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// result.Value is the Rocket RSI
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}
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// Batch
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TSeries results = Rrsi.Batch(series);
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// Span
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Rrsi.Batch(source, output, smoothLength: 10, rsiLength: 10);
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```
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## References
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- Ehlers, J. F. (2018). "Rocket RSI." *Technical Analysis of Stocks & Commodities*, May 2018.
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- Ehlers, J. F. (2004). *Cybernetic Analysis for Stocks and Futures*. Wiley.
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