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Miha Kralj
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- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
64 lines
4.3 KiB
Markdown
64 lines
4.3 KiB
Markdown
# CRSI: Connors RSI
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Connors RSI is a composite momentum oscillator that combines three independent measurements of price behavior into a single bounded (0-100) output: a short-term RSI of price, an RSI of the consecutive up/down streak length, and a percentile rank of the current rate of change within its recent history. The equal-weighted average of these three components produces a mean-reverting oscillator where extreme readings (above 90 or below 10) identify statistically overbought or oversold conditions with higher reliability than single-component RSI alone.
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## Historical Context
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Larry Connors and Cesar Alvarez introduced Connors RSI in their 2012 publication, building on Connors' earlier research into short-term mean reversion strategies. The indicator addressed a recognized weakness of standard RSI: its tendency to remain in overbought or oversold territory during strong trends without providing actionable reversal signals. By combining three orthogonal measurements of price behavior, each capturing a different aspect of momentum, CRSI reduces the false signal rate inherent in any single oscillator. The streak RSI component was particularly novel, converting the categorical information of consecutive up/down days into a continuous oscillator via a second RSI application. The percent rank component adds a non-parametric statistical dimension that is robust to distribution assumptions. Connors' backtesting showed the composite outperformed standard RSI for mean-reversion entry timing on equity indices and ETFs.
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## Architecture & Physics
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### Three-Component Pipeline
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CRSI combines three independent calculations with equal weighting:
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1. **Price RSI** (Component 1): Standard Wilder RSI with exponential smoothing ($\alpha = 1/\text{rsiPeriod}$) applied to the source series. Uses warmup compensation via the decaying exponential $e = \beta^n$ to correct for initial bias, producing valid output from bar 1.
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2. **Streak RSI** (Component 2): First computes a consecutive streak counter (positive for up-closes, negative for down-closes, zero for unchanged), then applies the same Wilder RSI to the streak series. This converts run-length information into a bounded oscillator.
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3. **Percent Rank** (Component 3): Computes 1-bar ROC, stores in a circular buffer, then counts what percentage of historical ROC values are less than or equal to the current ROC. This is a non-parametric ranking that is distribution-free.
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### Warmup Compensation
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Both RSI stages use the "section 2" warmup pattern: track $e = \beta^n$ and apply correction factor $c = 1/(1 - e)$ to the raw exponential averages until $e$ drops below $10^{-10}$. This eliminates the startup bias that plagues naive EMA initialization.
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### Final Composition
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The three components are averaged and clamped to $[0, 100]$:
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$$\text{CRSI} = \text{clamp}\!\left(\frac{\text{PriceRSI} + \text{StreakRSI} + \text{PctRank}}{3}, 0, 100\right)$$
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## Mathematical Foundation
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**Component 1: Price RSI** with Wilder smoothing ($\alpha = 1/p_1$):
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$$\overline{G}_t = \alpha \cdot \max(\Delta x_t, 0) + (1-\alpha) \cdot \overline{G}_{t-1}$$
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$$\overline{L}_t = \alpha \cdot \max(-\Delta x_t, 0) + (1-\alpha) \cdot \overline{L}_{t-1}$$
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$$RSI_1 = \frac{100 \cdot \overline{G}_t}{\overline{G}_t + \overline{L}_t}$$
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**Component 2: Streak counter** then RSI:
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$$\text{streak}_t = \begin{cases} \text{streak}_{t-1} + 1 & \text{if } x_t > x_{t-1} \text{ and streak}_{t-1} \geq 0 \\ 1 & \text{if } x_t > x_{t-1} \text{ and streak}_{t-1} < 0 \\ \text{streak}_{t-1} - 1 & \text{if } x_t < x_{t-1} \text{ and streak}_{t-1} \leq 0 \\ -1 & \text{if } x_t < x_{t-1} \text{ and streak}_{t-1} > 0 \\ 0 & \text{otherwise} \end{cases}$$
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$$RSI_2 = \text{Wilder\_RSI}(\text{streak}_t, p_2)$$
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**Component 3: Percent Rank** of 1-bar ROC over window $p_3$:
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$$ROC_t = \frac{x_t - x_{t-1}}{x_{t-1}} \times 100$$
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$$PctRank_t = \frac{|\{ROC_i : ROC_i \leq ROC_t,\; i \in \text{window}\}|}{|\text{window}|} \times 100$$
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**Composite:**
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$$CRSI_t = \frac{RSI_1 + RSI_2 + PctRank}{3}$$
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**Default parameters:** rsiPeriod = 3, streakPeriod = 2, rankPeriod = 100.
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## Resources
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- Connors, L. & Alvarez, C. (2012). *An Introduction to ConnorsRSI*. TradingMarkets
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- Connors, L. (2009). *Short-Term Trading Strategies That Work*. TradingMarkets
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- PineScript reference: [`crsi.pine`](crsi.pine)
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