How is the Laguerre RSI different from standard RSI?

Standard RSI averages gains and losses over a fixed lookback; the Laguerre version computes the same style of ratio from the outputs of a four-stage Laguerre filter, tuned by a damping factor instead of a period. It runs 0 to 1 rather than 0 to 100, plots much smoother at comparable responsiveness, and spends long stretches pinned at its extremes during trends.

What gamma value should I use for the Laguerre RSI?

There is no universally best value. Gamma runs from 0 to 1: lower values make the oscillator faster and noisier, higher values make it smoother and slower, with settings around 0.5 to 0.8 the most common starting points. The right choice depends on timeframe and market character, and some implementations adapt gamma automatically from measured volatility.

Why does the Laguerre RSI pin at 0 or 1?

Because its up and down sums come from the gaps between filter stages, and in a persistent move all the gaps point the same way. With the down-sum near zero the ratio saturates at 1, and it stays there until the stages actually compress and cross, which requires real countermovement. Standard RSI rarely saturates because its fixed window always contains a mix of gains and losses. Treat the pinning as a trend-persistence reading.

Are 0.8 and 0.2 overbought and oversold levels?

They are decision thresholds, not classic reversal zones. Above 0.8 does not mean stretched and due to fall; it usually means a strong advance in progress. The tradeable events are the exits from those regions, the drop back through 0.8 or the recovery through 0.2, and in trending conditions the mean-reversion reading of the thresholds is the fastest way to fight a market that keeps going.

What is the Fractals Energy or self-adjusting Laguerre RSI?

A variant, popularized on the Library by everget, that measures market choppiness (often called fractal energy or efficiency) each bar and feeds it into the damping factor. In congested conditions the oscillator slows down, filtering noise; in clean directional moves it speeds up, tracking the trend closely. It automates the gamma-tuning judgment at the cost of a second layer of estimation.

Can the Laguerre RSI be applied to inputs other than price?

Yes. The cascade accepts any reasonably scaled series, so implementations run it on alternative sources or even on other indicators, the same trick as RSI of other sources. Applying it to an already-smoothed input compounds lag, so the common practice is to feed raw price or a lightly processed source and let the Laguerre structure do the smoothing.

Concept

Laguerre RSI

Laguerre RSI is a Momentum & Oscillators concept. The Library holds 1 implementation, a working definition you can pull into Quant.

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The top custom implementation, built on the original standard Laguerre RSI formula.

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Laguerre RSI

Indicator

What is the Laguerre RSI?

The Laguerre RSI is John Ehlers' reworking of RSI in which the lookback window is replaced by a four-stage Laguerre filter. Price runs through a cascade of four filter stages governed by a single damping factor, gamma, between 0 and 1. The RSI-style ratio of up moves to total moves is then computed from the differences between successive filter stages rather than from raw bar-to-bar changes, and the output is scaled 0 to 1.

The point of the Laguerre structure is time warping: with only four terms, the filter weights recent prices heavily while keeping a long decaying memory of older ones, something a plain moving average would need far more periods (and far more lag) to approximate. The result is an oscillator that plots very smooth yet still turns quickly, and that tends to pin near 1 in strong up-moves and near 0 in strong down-moves; 0.8 and 0.2 are the common decision thresholds.

Mechanically, each bar compares the four stage outputs pairwise: where a faster stage sits above the slower one below it, the gap adds to the up-sum, and where it sits below, to the down-sum. The plotted value is the up-sum divided by the total. In a persistent advance all three gaps stay positive, the down-sum starves, and the oscillator sits at or near 1 for as long as the move lasts; that pinning is information about trend persistence, not a malfunction. Ehlers published the design alongside the filter itself in his early-2000s Time Warp work and the Cybernetic Analysis book.

The Library carries the lineage from TheLark's early port through KivancOzbilgic's widely used version to everget's Fractals Energy variant, which measures how choppy the market is and feeds that into the damping factor, slowing the oscillator in congestion and quickening it in clean moves, an adaptive RSI in spirit. The honest caveats: the 0 to 1 pinning that makes it a good trend-hold tool makes classic overbought/oversold fading dangerous, and one gamma controls everything, so small setting changes move every behavior at once.

How to identify the Laguerre RSI on a chart

It reads like an RSI with smoother manners: same idea, different scale. The tells are quick to check.

1Check the scale: 0 to 1 with decision lines at 0.8 and 0.2, instead of RSI's 0 to 100 with 70/30.
2Check the input: a single gamma (or an adaptive alpha) rather than a bar-count length.
3Watch the character: long flat stretches pinned near 1 in advances and near 0 in declines, with smooth, rounded transitions between them.
4Confirm the construction where source is visible: up and down sums built from differences between four cascaded Laguerre stages.
5Read events at the thresholds: the drop back through 0.8 after a pinned stretch, or the cross up through 0.2, are the signals implementations act on, sometimes with divergence as a secondary read.

How it's calculated

A momentum oscillator between 0 and 1 that measures up versus down pressure across the stages of a Laguerre-filtered price series instead of raw price changes.

L0_t = (1 - \gamma) \times P_t + \gamma \times L0_{t-1}

L1_t = -\gamma \times L0_t + L0_{t-1} + \gamma \times L1_{t-1}

L2_t = -\gamma \times L1_t + L1_{t-1} + \gamma \times L2_{t-1}

L3_t = -\gamma \times L2_t + L2_{t-1} + \gamma \times L3_{t-1}

\operatorname{CU}_t = \max(L0_t - L1_t, 0) + \max(L1_t - L2_t, 0) + \max(L2_t - L3_t, 0)

\operatorname{CD}_t = \max(L1_t - L0_t, 0) + \max(L2_t - L1_t, 0) + \max(L3_t - L2_t, 0)

\operatorname{LaRSI}_t = \frac{\operatorname{CU}_t}{\operatorname{CU}_t + \operatorname{CD}_t} \text{ when } \operatorname{CU}_t + \operatorname{CD}_t > 0\text{, otherwise the prior value holds}

P_t: source price at bar t (Ehlers used the bar midpoint, high plus low over 2; close is a common default)

t: bar index (t-1 is the prior bar)

gamma: Laguerre damping factor between 0 and 1 (Ehlers used 0.5; larger values give a smoother, slower output)

L0_t: stage 0 of the Laguerre filter (the input stage)

L1_t: stage 1 of the Laguerre filter

L2_t: stage 2 of the Laguerre filter

L3_t: stage 3 of the Laguerre filter

CU_t: summed upward pressure across adjacent filter stages

CD_t: summed downward pressure across adjacent filter stages

LaRSI_t: Laguerre RSI value at bar t, between 0 and 1

Some implementations take alpha = 1 - gamma as the input, and many rescale the output to a 0 to 100 range.

Common signal levels are 0.8 overbought and 0.2 oversold (80 and 20 when rescaled).

Introduced by John Ehlers in Cybernetic Analysis for Stocks and Futures; initialize L0 through L3 to the first price to limit warm-up artifacts.

How traders use it

As a trend-hold read: the oscillator staying pinned above 0.8 marks a persistent up-move, and the drop back below that level is used as an exhaustion or exit cue, mirrored at 0.2 for down-moves.
As a reversal trigger in range conditions: crossing back up through 0.2 or down through 0.8 gives mean-reversion entries, best filtered by a regime check since those signals fail badly in trends.
As a one-knob oscillator: gamma alone sets responsiveness, lower values reacting faster and higher values smoothing harder, which is why adaptive variants tie gamma to a volatility or fractal-energy measure.
As a location-gated trigger: taking the 0.2 cross-up only at mapped support, or the 0.8 cross-down only at resistance, converts a generic oscillator event into a level-confirmation tool.
As the fast layer in oscillator stacks: its smoothness at speed makes it a common companion to slower fixed-window reads, flagging turns early that the standard oscillator confirms later.

Laguerre RSI vs related oscillators

RSI: Standard RSI averages gains and losses over a fixed window and rarely reaches its extremes; the Laguerre version computes the same style of ratio from a warped-memory filter, plots far smoother, and spends whole trends pinned at 0 or 1. Same ratio idea, opposite temperament at the extremes.

Stochastic RSI: Both answer the complaint that RSI feels sluggish, from opposite directions. Stochastic RSI stretches RSI's range and amplifies its noise; the Laguerre RSI suppresses noise while keeping speed. One buys sensitivity with whipsaw, the other buys smoothness with pinning.

Adaptive/dynamic RSI: Adaptive RSIs keep the classic formula and vary the lookback with conditions. The Laguerre RSI discards the lookback entirely for a filter cascade. The Fractals Energy variant merges the two ideas by driving the Laguerre damping factor from a measured choppiness input.

Concept family

Momentum & Oscillators

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