RSI adaptive zones [AdaptiveRSI]

This script introduces a unified mathematical framework that auto-scales oversold/overbought and support/resistance zones for any period length. It also adds true RSI candles for spotting intrabar signals.

Built on the Logit RSI foundation, this indicator converts RSI into a statistically normalized space, allowing all RSI lengths to share the same mathematical footing.
What was once based on experience and observation is now grounded in math.

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💡 Example Use Cases

1. RSI(14): Classic overbought/oversold signals + divergence
   
2. Support in an uptrend using RSI(14)
   
3. Range breakouts using RSI(21)
   
4. Short-term pullbacks using RSI(5)
   

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THE PAST: RSI Interpretation Required Multiple Rulebooks

Over decades, RSI practitioners discovered that RSI behaves differently depending on trend and lookback length:
• In uptrends, RSI tends to hold higher support zones (40–50)
• In downtrends, RSI tends to resist below 50–60
• Short RSIs (e.g., RSI(2)) require far more extreme threshold values
• Longer RSIs cluster near the center and rarely reach 70/30

These observations were correct — but lacked a unifying mathematical explanation.

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THE PRESENT: One Framework Handles RSI(2) to RSI(200)

Instead of using fixed thresholds (70/30, 90/10, etc.), this indicator maps RSI into a normalized statistical space using:

• The Logit transformation to remove 0–100 scale distortion
• A universal scaling based on 2/√(n−1) scaling factor to equalize distribution shapes

As a result, RSI values become directly comparable across all lookback periods.

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💡 How the Adaptive Zones Are Calculated

The adaptive framework defines RSI zones as statistical regimes derived from the Logit-transformed RSI.
Each boundary corresponds to a standard deviation (σ) threshold, scaled by 2/√(n−1), making RSI distributions comparable across periods.

This structure was inspired by Nassim Nicholas Taleb’s body–shoulders–tails regime model:

• Body (±0.66σ) — consolidation / equilibrium
  
• Shoulders (±1σ to ±2.14σ) — trending region
  
• Tails (outside of ±2.14σ) — rare, high-volatility behavior
  

Transitions between these regimes are defined by the derivatives of the position (CDF) function:
• ±1σ → shift from consolidation to trend
• ±√3σ → shift from trend to exhaustion



Adaptive Zone Summary

• Consolidation: −0.66σ to +0.66σ
  
• Support/Resistance: ±0.66σ to ±1σ
  
• Uptrend/Downtrend: ±1σ to ±√3σ
  
• Overbought/Oversold: ±√3σ to ±2.14σ
  
• Tails: outside of ±2.14σ
  

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📌 Inverse Transformation: From σ-Space Back to RSI

A final step is required to return these statistically normalized boundaries back into the familiar 0–100 RSI scale. Because the Logit transform maps RSI into an unbounded real-number domain, the inverse operation uses the hyperbolic tangent function to compress σ-space back into the bounded RSI range.

RSI(n) = 50 + 50 · tanh(z / √(n − 1))

The result is a smooth, mathematically consistent conversion where the same statistical thresholds maintain identical meaning across all RSI lengths, while still expressing themselves as intuitive RSI values traders already understand.



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Key Features

• Mathematically derived adaptive zones for any RSI period
  
• Support/resistance zone identification for trend-aligned reversals
  
• Optional OHLC RSI bars/candles for intrabar zone interactions
  
• Fully customizable zone visibility and colors
  
• Statistically consistent interpretation across all markets and timeframes
  

Inputs

1. RSI Length — core parameter controlling zone scaling
   
2. RSI Display: Line / Bar / Candle visualization modes
   

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💡 How to Use

This indicator is a framework, not a binary signal generator.
Start by defining the question you want answered, e.g.:

• Where is the breakout?
• Is price overextended or still trending?
• Is the correction ending, or is trend reversing?

Then:

1. Choose the RSI length that matches your timeframe
   
2. Observe which adaptive zone price is interacting with
   
3. Interpret market behavior accordingly
   

Example: Long-Term Trend Assesment using RSI(200)
A trader may ask: "Is this a long term top?"
Unlikely, because RSI(200) holds above Resistance zone, therefore the trend remains strong.



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👉 Practical tip:
If you used to overlay weekly RSI(14) on a daily chart (getting a line that waits 5 sessions to recalculate), you can now read the same long-horizon state continuously: set RSI(70) on the daily chart (~14 weeks × 5 days/week = 70 days) and let the adaptive zones update every bar.
Note: It won’t be numerically identical to the weekly RSI due to lookback period used, but it tracks the same regime on a standardized scale with bar-by-bar updates.

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Note: This framework describes statistical structure, not prediction. Use as part of a complete trading approach. Past behavior does not guarantee future outcomes.

framework ≠ guaranteed signal

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Attribution & License
This indicator incorporates:
• Logit transformation of RSI
• Variance scaling using 2/√(n−1)
• Zone placement derived from Taleb’s body–shoulders–tails regime model and CDF derivatives
• Inverse TANH(z) transform for mapping z-scores back into bounded RSI space

Released under CC BY-NC-SA 4.0 — free for non-commercial use with credit.
© AdaptiveRSI