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Ehlers Autocorrelation

Ehlers DSP cycle spectral ehlers dsp dominant-cycle

Computes Pearson correlation of smoothed price with its lags to identify market structure.

Visual Example

Ehlers Autocorrelation — 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

Computes Pearson correlation of smoothed price with its lags to identify market structure.

Use to generate an autocorrelation periodogram showing which cycle periods are currently dominant. Visualise as a heatmap to track cycle period shifts over time.

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 introduces autocorrelation-based cycle measurement in Cycle Analytics for Traders (2013) as a more robust alternative to DFT. By computing autocorrelation of Roofing-filtered price at each lag, then applying a spectral DFT to the lag series, he obtains a periodogram insensitive to amplitude variations.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 20+ 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/ehlers_autocorrelation.rs):

\[ \rho(lag) = \frac{N \sum X Y - \sum X \sum Y}{\sqrt{(N \sum X^2 - (\sum X)^2)(N \sum Y^2 - (\sum Y)^2)}} \]

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

Parameters

Parameter Default Description
length 20 Correlation window length
num_lags 100 Number of lags to compute

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::EHLERS_AUTOCORRELATION;
use quantwave_core::traits::Next;

let mut ind = EHLERS_AUTOCORRELATION::new(20);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import EHLERS_AUTOCORRELATION

ind = EHLERS_AUTOCORRELATION(20)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_ehlers_autocorrelation(series: pl.Series) -> pl.Series:
    ind = qw.EHLERS_AUTOCORRELATION(20)
    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_ehlers_autocorrelation, return_dtype=pl.Float64).alias("ehlers_autocorrelation")
    )
    .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’ TIPS - FEBRUARY 2025.html

Implementation: quantwave-core/src/indicators/ehlers_autocorrelation.rs (EHLERS_AUTOCORRELATION / EHLERS_AUTOCORRELATION_METADATA). Parity: quantwave-core/tests/gold_standard/ehlers_autocorrelation.json

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