QuanTAlib/lib/cycles/eacp/eacp.md

EACP: Ehlers Autocorrelation Periodogram

"The autocorrelation periodogram uses the Wiener-Khinchin theorem to transform autocorrelation into spectral density, revealing the dominant cycle hidden within price noise."

The Ehlers Autocorrelation Periodogram (EACP) is an advanced spectral analysis tool that estimates the dominant cycle period of a financial time series. It computes autocorrelation across various lags and transforms this into a power spectrum to identify the most potent frequency, enabling adaptive indicator tuning.

Historical Context

John Ehlers introduced the Autocorrelation Periodogram to the trading community as a solution for measuring market cycles. He leveraged the Wiener-Khinchin theorem, which links the time domain (autocorrelation) to the frequency domain (power spectral density).

This allows traders to detect the current "heartbeat" of the market—the dominant cycle—which can then tune other indicators (like RSI or Stochastic) to the current market speed, creating truly adaptive trading systems.

Architecture & Physics

The algorithm proceeds in three major stages: Pre-filtering, Correlation, and Spectral Analysis.

1. Signal Pre-processing

High-pass filter removes DC component and trends; Super-smoother attenuates aliasing noise.

HP_t = (1 - \alpha_{HP}/2)^2 \cdot (P_t - 2P_{t-1} + P_{t-2}) + 2(1-\alpha_{HP}) \cdot HP_{t-1} - (1-\alpha_{HP})^2 \cdot HP_{t-2}

2. Autocorrelation

For every lag k from 0 to MaxPeriod:

R_k = \frac{\sum (x_i - \bar{x})(x_{i-k} - \bar{x})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (x_{i-k} - \bar{x})^2}}

A high correlation at lag 20 implies a 20-bar cycle.

3. Dominant Cycle Extraction

Power spectrum via DFT, smoothed with exponential decay:

S_p = 0.2 \cdot P_p^2 + 0.8 \cdot S_{p-1}

Dominant cycle as center of gravity of spectral peaks:

DC = \frac{\sum Power_i \cdot Period_i}{\sum Power_i}

Performance Profile

Operation Count (Streaming Mode, per Bar)

Operation	Count	Cost (cycles)	Subtotal
Correlation loop	N×M	5	5NM
DFT inner loop	N×N	8	8N²
Power smoothing	N	4	4N
AGC normalization	N	3	3N
Total	—	—	O(N²)

Complexity Analysis

• Streaming: O(N × M) where N=period range, M=averaging length
• Memory: O(N) for correlation and power arrays
• Warmup: ~2 × MaxPeriod bars

Note: This is one of the most computationally expensive indicators due to nested loops.

Validation

Library	Status	Notes
TA-Lib	N/A	Not implemented
Skender	N/A	Not implemented
PineScript	✅	Validated against Ehlers' reference code

Usage & Pitfalls

• Primary use is tuning—provides period parameter for other indicators (RSI, Stochastic)
• Requires substantial warmup (~2 × MaxPeriod) to stabilize spectrum
• Struggles with rapid cycle changes—period jumping from 10 to 40 in few bars
• Compute on bar close only—avoid running on every tick for many symbols
• Enhance mode (enhance=true) sharpens peaks but can cause jumpiness
• Pure sine wave of period 20 correctly converges to ~20.0

API

classDiagram
    class Eacp {
        +int MinPeriod
        +int MaxPeriod
        +double DominantCycle
        +double NormalizedPower
        +bool IsHot
        +Eacp(int minPeriod, int maxPeriod, bool enhance)
        +TValue Update(TValue input, bool isNew)
        +void Reset()
    }

Class: Eacp

Parameter	Type	Default	Range	Description
minPeriod	int	8	≥3	Minimum period to evaluate
maxPeriod	int	48	>minPeriod	Maximum period to evaluate
enhance	bool	true	—	Apply cubic emphasis to peaks

Properties

• DominantCycle (double): Estimated dominant cycle period in bars
• NormalizedPower (double): Power at dominant period (0-1)
• IsHot (bool): Returns true when warmup is complete

Methods

• Update(TValue input, bool isNew): Updates the indicator with a new data point

C# Example

using QuanTAlib;

// Configure for cycles between 8 and 48 bars
var eacp = new Eacp(minPeriod: 8, maxPeriod: 48, enhance: true);

// Update with streaming data
foreach (var bar in quotes)
{
    var result = eacp.Update(new TValue(bar.Date, bar.Close));
    
    if (eacp.IsHot)
    {
        Console.WriteLine($"{bar.Date}: Dominant Cycle = {eacp.DominantCycle:F1} bars");
        
        // Use cycle to tune RSI
        int adaptivePeriod = (int)(eacp.DominantCycle / 2);
        var adaptiveRsi = new Rsi(adaptivePeriod);
    }
}

// Batch calculation
var output = Eacp.Calculate(sourceSeries, minPeriod: 8, maxPeriod: 48);