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Laguerre Oscillator

Ehlers DSP oscillator ehlers dsp laguerre momentum

A low-lag trend oscillator derived from Laguerre polynomials and normalized by RMS volatility.

Visual Example

Laguerre Oscillator — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

A low-lag trend oscillator derived from Laguerre polynomials and normalized by RMS volatility.

Use to detect overbought and oversold conditions with very low lag. The single gamma parameter lets you tune it from aggressive to smooth.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

Ehlers describes the Laguerre Oscillator in Cybernetic Analysis as measuring the difference between the first and last elements of a 4-element Laguerre filter bank, extracting the high-frequency component as a zero-lag momentum measure.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 30+ bars warm-up for filter state to stabilise
  • Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/laguerre_oscillator.rs):

[ L_0 = UltimateSmoother(Close, Length) ] [ L_1 = -\gamma L_0 + L_{0,t-1} + \gamma L_{1,t-1} ] [ RMS = \sqrt{\frac{1}{n}\sum (L_0 - L_1)^2} ] [ Osc = (L_0 - L_1) / RMS ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/laguerre_oscillator.json.

Parameters

Parameter Default Description
length 30 UltimateSmoother period
gamma 0.5 Smoothing factor
rms_period 100 RMS normalization period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::LAGUERRE_OSCILLATOR;
use quantwave_core::traits::Next;

let mut ind = LAGUERRE_OSCILLATOR::new(30);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import LAGUERRE_OSCILLATOR

ind = LAGUERRE_OSCILLATOR(30)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_laguerre_oscillator(series: pl.Series) -> pl.Series:
    ind = qw.LAGUERRE_OSCILLATOR(30)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_laguerre_oscillator, return_dtype=pl.Float64).alias("laguerre_oscillator")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
  • Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
  • Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
  • Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/traderstipsreference/TRADERS%E2%80%99%20TIPS%20-%20JULY%202025.html

Implementation: quantwave-core/src/indicators/laguerre_oscillator.rs (LAGUERRE_OSCILLATOR / LAGUERRE_OSCILLATOR_METADATA). Parity: quantwave-core/tests/gold_standard/laguerre_oscillator.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.