QuanTAlib/lib/cycles/epa/epa.md

EPA — Ehlers Phasor Analysis

Overview

EPA (Ehlers Phasor Analysis) extracts cycle phase from price data by computing a phasor using Pearson correlation of a price window against cosine and negative-sine reference waves. The angle of the phasor reveals the current phase position within the dominant cycle, enabling identification of cycle valleys (at −90°) and peaks (at +90°), as well as determining whether the market is cycling or trending.

Property	Value
Category	Cycles
Author	John F. Ehlers
Source	TASC November 2022, "Recurring Phase Of Cycle Analysis"

Origin and Sources

John Ehlers introduced Phasor Analysis in the November 2022 issue of Stocks & Commodities magazine in the article "Recurring Phase Of Cycle Analysis." The technique uses Pearson correlation as a matched filter to determine how well price data correlates with cosine and sine waves at a presumed cycle period, producing the Real and Imaginary components of a phasor.

Function Signature

// streaming
var epa = new Epa(period: 28);
TValue result = epa.Update(tValue);

// static batch (TSeries)
TSeries output = Epa.Batch(source, period: 28);

// static batch (Span)
Epa.Batch(source, output, period: 28);

// factory
var (results, indicator) = Epa.Calculate(source, period: 28);

Parameters

Parameter	Type	Default	Valid Range	Description
period	int	28	> 1	Presumed dominant cycle wavelength in bars

Outputs

Output	Type	Description
Angle	double	Phasor angle in degrees with wraparound compensation
DerivedPeriod	double	Cycle period derived from angle rate-of-change (clamped to 60)
TrendState	int	+1 = trending long, −1 = trending short, 0 = cycling

The primary output (Last.Value) is the Angle.

Algorithm

1. Dual Pearson Correlation over a sliding window of period bars:

   • Real = corr(price, cos(2πk/N)) — correlation with cosine
   • Imag = corr(price, -sin(2πk/N)) — correlation with negative sine

2. Angle Calculation: Angle = 90° - atan(Imag/Real) with quadrant fix: if Real < 0, subtract 180°.

3. Wraparound Compensation: When the angle crosses the 360° boundary (previous angle > 90° and current < −90°), subtract 360° to maintain continuity.

4. Monotonic Constraint: The angle generally cannot decrease, but allows exceptions at extreme regions (when both previous and current angles are in the same deep-negative quadrant).

5. Derived Period: Computed as 360 / ΔAngle where ΔAngle is the per-bar angle change. When ΔAngle ≤ 0, the previous delta is used. The result is clamped to a maximum of 60.

6. Trend State: When the angle rate-of-change ≤ 6°/bar:

   • If angle ≥ 90° or ≤ −90° → +1 (trending long)
   • If −90° < angle < 90° → −1 (trending short)
   • Otherwise → 0 (cycling)

Interpretation

• The phasor angle oscillates between −180° and +180°, completing one full cycle per dominant period.
• Cycle valleys correspond to the angle crossing −90°.
• Cycle peaks correspond to the angle near +90°.
• The TrendState indicates when the market transitions from cycling to trending behavior based on the angle rate slowing.
• The DerivedPeriod provides a real-time estimate of the dominant cycle length.

Properties

Property	Value
Complexity	O(period) per bar
Memory	O(period) — RingBuffer + trig tables
Warmup	period bars
Output Range	Angle: unbounded; DerivedPeriod: [0, 60]; TrendState: {−1, 0, +1}
Zero Alloc	✅ Hot path allocates nothing

Related Indicators

• CCOR — Ehlers Correlation Cycle (TASC June 2020) — earlier version with simpler angle logic
• HT_PHASOR — Hilbert Transform Phasor Components — different algorithm
• FSI — Ehlers Fourier Series Indicator
• EBSW — Ehlers Even Better Sine Wave