Laguerre RSI

The Laguerre RSI is an advanced technical momentum indicator developed by aerospace engineer and trader John Ehlers. It improves upon the traditional Relative Strength Index (RSI) by applying a mathematical smoothing technique called a Laguerre filter.

The goal of the Laguerre RSI is to solve a common problem in technical analysis: the trade-off between smoothing out market noise and lagging behind real-time price action. By using this specific filter, the indicator provides a much smoother line that still reacts quickly to sudden price changes.

How It Differs from Classic RSI

While Welles Wilder's classic RSI uses a standard moving average to calculate gains and losses, Ehlers' version completely replaces that smoothing mechanism.

• The Scale: The Laguerre RSI typically oscillates between $0$ and $1$ (though some platforms scale it from $0$ to $100$).
• The Extremes: Because it is more responsive, the standard overbought and oversold levels are tightened to $0.8$ (overbought) and $0.2$ (oversold), compared to the classic $70/30$ levels.
• The "Lock-to-Lock" Movement: The Laguerre RSI tends to move rapidly from one extreme to the other (e.g., from $0.2$ straight to $0.8$) and stay pinned there during strong trends, filtering out the jagged false signals common in the standard RSI.
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The Gamma Factor

The core of the indicator is a four-pole filter that generates four intermediate values ($L_0, L_1, L_2, L_3$). Instead of a traditional "lookback period" (like a 14-day RSI), the Laguerre RSI uses a single damping parameter called Gamma ($\gamma$), which is usually set between $0.1$ and $0.9$.

• Higher Gamma (e.g., $0.7$ - $0.8$): Provides a smoother line with less noise, but introduces slightly more lag. Best for higher timeframes.
• Default Gamma ($0.5$): The standard balance between responsiveness and smoothness.
• Lower Gamma (e.g., $0.2$ - $0.3$): Highly sensitive and fast to react, but will produce more false signals. Best for short-term scalping.

You can see how adjusting the Gamma parameter fundamentally changes the indicator's behavior below:

Key insight: Because it uses a recursive feedback loop (where the current value relies heavily on the previous value), adjusting the Gamma factor acts like a time-warp—allowing the indicator to look at a longer "effective" period without the usual delay.

How to Trade with the Laguerre RSI

Because the indicator is so fast, traders usually use it for mean reversion or trend pullbacks.

• Mean Reversion: Buy when the indicator drops below $0.2$ and sharply crosses back above it. Sell when it rises above $0.8$ and crosses back below it.

• Trend Pullbacks: If a higher-timeframe trend is bullish, traders will wait for the Laguerre RSI to briefly dip toward $0.2$ on a lower timeframe and buy the bounce, ignoring sell signals entirely.

• Midpoint Bias: Some systematic traders simply use the $0.5$ midpoint as a momentum filter: staying above $0.5$ indicates bullish momentum, while staying below $0.5$ indicates bearish momentum.

You can download this explainer here:

https://docs.google.com/document/d/1v747E6VGq8z-ySB5yyQt_LIJLwKFmD-ovAOVXW3HxKA/edit?usp=drive_link