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FourierSeriesModel

Ehlers DSP cycle spectral ehlers prediction fourier

Synthesized market model using fundamental and harmonic frequency components.

Visual Example

FourierSeriesModel — 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 FourierSeriesModel indicator is a technical analysis tool that synthesized market model using fundamental and harmonic frequency components.

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 to model price as a sum of sine wave harmonics for short-term prediction. Most effective in clearly cyclical markets; combine with a cycle mode detector to disable it in trends.

The Fourier Series Model fits harmonically related sine waves to recent price history using least-squares coefficients. Ehlers shows that projecting this model one bar forward gives a price forecast useful for anticipatory entry timing at predicted cycle turns.

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/fourier_series.rs):

[ BP_k = \text{BandPass}(Price, Fundamental/k) ] [ Q_k = \frac{Fundamental}{2\pi} (BP_{k} - BP_{k,t-1}) ] [ P_k = \sum_{n=0}^{F-1} (BP_{k,t-n}^2 + Q_{k,t-n}^2) ] [ Wave = BP_1 + \sqrt{P_2/P_1}BP_2 + \sqrt{P_3/P_1}BP_3 ]

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

Parameters

Parameter Default Description
fundamental 20 Fundamental cycle period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::FOURIER_SERIES_MODEL;
use quantwave_core::traits::Next;

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

Streaming (Python)

from quantwave import FOURIER_SERIES_MODEL

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

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_fourierseriesmodel(series: pl.Series) -> pl.Series:
    ind = qw.FOURIER_SERIES_MODEL(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_fourierseriesmodel, return_dtype=pl.Float64).alias("fourierseriesmodel")
    )
    .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/FOURIER%20SERIES%20MODEL%20OF%20THE%20MARKET.pdf

Implementation: quantwave-core/src/indicators/fourier_series.rs (FOURIER_SERIES_MODEL / FOURIER_SERIES_MODEL_METADATA). Parity: quantwave-core/tests/gold_standard/fourier_series_model.json

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