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Zero Lag EC

Ehlers DSP moving-average zero-lag ehlers ema smoothing

Zero Lag Error Corrected EMA attempts to eliminate lag by adding an error term to the EMA.

Visual Example

Zero Lag EC — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Zero Lag EC indicator is a technical analysis tool that zero lag error corrected ema attempts to eliminate lag by adding an error term to the ema.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use as a near-zero-lag moving average for trend-following systems. The error-correction term removes the lag inherent in the standard EMA without introducing significant overshoot.

Ehlers introduces the Zero Lag indicator in Cybernetic Analysis as an EMA with an added error-correction term that subtracts the average lag from the output. The resulting EC (Error Corrected) line tracks price with near-zero delay while the ZL-EMA provides a smoothed reference, with crossovers between them providing trade signals.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

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

[ \alpha = \frac{2}{Length + 1} ] [ EMA = \alpha \times Close + (1 - \alpha) \times EMA_{t-1} ] [ EC = \alpha \times (EMA + Gain \times (Close - EC_{t-1})) + (1 - \alpha) \times EC_{t-1} ]

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

Parameters

Parameter Default Description
length 20 Equivalent SMA length
gain_limit 50.0 Gain limit (divided by 10 for actual gain)

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::ZERO_LAG;
use quantwave_core::traits::Next;

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

Streaming (Python)

from quantwave import ZERO_LAG

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

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_zero_lag_ec(series: pl.Series) -> pl.Series:
    ind = qw.ZERO_LAG(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_zero_lag_ec, return_dtype=pl.Float64).alias("zero_lag_ec")
    )
    .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/Ehlers%20Papers/implemented/ZeroLag.pdf

Implementation: quantwave-core/src/indicators/zero_lag.rs (ZERO_LAG / ZERO_LAG_METADATA). Parity: quantwave-core/tests/gold_standard/zero_lag.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.