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Miha Kralj
93 lines
4.6 KiB
Markdown
93 lines
4.6 KiB
Markdown
# EPA — Ehlers Phasor Analysis
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## Overview
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**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.
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| Property | Value |
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|:-------------- |:------------------------------- |
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| **Category** | Cycles |
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| **Author** | John F. Ehlers |
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| **Source** | TASC November 2022, "Recurring Phase Of Cycle Analysis" |
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## Origin and Sources
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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.
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## Function Signature
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```csharp
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// streaming
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var epa = new Epa(period: 28);
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TValue result = epa.Update(tValue);
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// static batch (TSeries)
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TSeries output = Epa.Batch(source, period: 28);
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// static batch (Span)
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Epa.Batch(source, output, period: 28);
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// factory
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var (results, indicator) = Epa.Calculate(source, period: 28);
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```
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## Parameters
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| Parameter | Type | Default | Valid Range | Description |
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|:---------- |:----- |:------- |:----------- |:-------------------------------------------- |
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| `period` | int | 28 | > 1 | Presumed dominant cycle wavelength in bars |
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## Outputs
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| Output | Type | Description |
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|:--------------- |:------ |:--------------------------------------------------------------- |
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| `Angle` | double | Phasor angle in degrees with wraparound compensation |
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| `DerivedPeriod` | double | Cycle period derived from angle rate-of-change (clamped to 60) |
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| `TrendState` | int | +1 = trending long, −1 = trending short, 0 = cycling |
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The primary output (`Last.Value`) is the **Angle**.
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## Algorithm
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1. **Dual Pearson Correlation** over a sliding window of `period` bars:
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- `Real = corr(price, cos(2πk/N))` — correlation with cosine
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- `Imag = corr(price, -sin(2πk/N))` — correlation with negative sine
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2. **Angle Calculation**: `Angle = 90° - atan(Imag/Real)` with quadrant fix: if `Real < 0`, subtract 180°.
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3. **Wraparound Compensation**: When the angle crosses the 360° boundary (previous angle > 90° and current < −90°), subtract 360° to maintain continuity.
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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).
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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.
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6. **Trend State**: When the angle rate-of-change ≤ 6°/bar:
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- If angle ≥ 90° or ≤ −90° → **+1** (trending long)
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- If −90° < angle < 90° → **−1** (trending short)
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- Otherwise → **0** (cycling)
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## Interpretation
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- The phasor angle oscillates between −180° and +180°, completing one full cycle per dominant period.
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- **Cycle valleys** correspond to the angle crossing −90°.
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- **Cycle peaks** correspond to the angle near +90°.
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- The **TrendState** indicates when the market transitions from cycling to trending behavior based on the angle rate slowing.
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- The **DerivedPeriod** provides a real-time estimate of the dominant cycle length.
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## Properties
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| Property | Value |
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|:-------------- |:------------------------------------------- |
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| Complexity | O(period) per bar |
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| Memory | O(period) — RingBuffer + trig tables |
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| Warmup | `period` bars |
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| Output Range | Angle: unbounded; DerivedPeriod: [0, 60]; TrendState: {−1, 0, +1} |
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| Zero Alloc | ✅ Hot path allocates nothing |
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## Related Indicators
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- [CCOR](../ccor/ccor.md) — Ehlers Correlation Cycle (TASC June 2020) — earlier version with simpler angle logic
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- [HT_PHASOR](../ht_phasor/ht_phasor.md) — Hilbert Transform Phasor Components — different algorithm
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- [FSI](../fsi/fsi.md) — Ehlers Fourier Series Indicator
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- [EBSW](../ebsw/ebsw.md) — Ehlers Even Better Sine Wave
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