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lib/cycles/ccor/Ccor.md
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# CCOR: Ehlers Correlation Cycle
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 20), `threshold` (default 9.0) |
| **Outputs** | Single series (Ccor) |
| **Output range** | Varies (see docs) |
| **Warmup** | `period` bars |
### TL;DR
- CCOR extracts cycle phase by computing Pearson correlation of a price window against cosine (Real) and negative-sine (Imaginary) reference waves of...
- Parameterized by `period` (default 20), `threshold` (default 9.0).
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
CCOR extracts cycle phase by computing Pearson correlation of a price window against cosine (Real) and negative-sine (Imaginary) reference waves of a presumed fixed period, converting the resulting phasor to an angle with a monotonic constraint, and classifying the market state as trending or cycling based on the angle rate of change. Unlike Hilbert Transform approaches that rely on analytic signal construction, CCOR uses the statistical machinery of correlation to measure how well price "fits" each quadrature component, yielding bounded $[-1, +1]$ outputs that double as confidence measures. The method was introduced to address the instability of Hilbert-based phasors during trend-dominated regimes.
## Historical Context
lib/cycles/ccyc/Ccyc.Validation.Tests.cs
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var ccycNoise = new Ccyc(0.07);
var ccycSine = new Ccyc(0.07);
var rng = new Random(42);
var rng = new GBM(startPrice: 100.0, sigma: 0.1, seed: 42);
double sineEnergy = 0;
for (int i = 0; i < 300; i++)
{
double noiseVal = 100 + rng.NextDouble() * 10;
double noiseVal = rng.Next().Close;
ccycNoise.Update(new TValue(DateTime.UtcNow.AddMinutes(i), noiseVal), true);
double sineVal = 100 + 10 * Math.Sin(2 * Math.PI * i / 20.0);
lib/cycles/ccyc/Ccyc.md
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# CCYC: Ehlers Cyber Cycle
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `alpha` (default 0.07) |
| **Outputs** | Single series (Ccyc) |
| **Output range** | Varies (see docs) |
| **Warmup** | `7` bars |
### TL;DR
- CCYC isolates the dominant cycle component from price data using a 2-pole high-pass IIR filter applied to a 4-tap FIR-smoothed input, producing an ...
- Parameterized by `alpha` (default 0.07).
- Output range: Varies (see docs).
- Requires `7` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
CCYC isolates the dominant cycle component from price data using a 2-pole high-pass IIR filter applied to a 4-tap FIR-smoothed input, producing an oscillator that strips trend while preserving cyclical content with minimal lag. The companion trigger line (one-bar delay of the cycle output) provides crossover signals for timing entries and exits. Unlike band-pass approaches that require specifying a center frequency, CCYC's high-pass architecture extracts whatever cyclic energy exists above a cutoff controlled by a single $\alpha$ damping parameter, making it adaptive to the dominant period present in the data.
## Historical Context
lib/cycles/cg/cg.md
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# CG: Ehlers Center of Gravity
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 10) |
| **Outputs** | Single series (Cg) |
| **Output range** | Varies (see docs) |
| **Warmup** | `period` bars |
### TL;DR
- CG identifies potential turning points using the physics concept of weighted center of mass applied to a price window.
- Parameterized by `period` (default 10).
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
CG identifies potential turning points using the physics concept of weighted center of mass applied to a price window. Developed by John Ehlers, the oscillator measures where the "weight" of prices is concentrated within a lookback period, producing a leading indicator that oscillates around zero with minimal lag compared to traditional moving average crossover systems.
## Historical Context
lib/cycles/dsp/dsp.md
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# DSP: Ehlers Detrended Synthetic Price
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 40) |
| **Outputs** | Single series (Dsp) |
| **Output range** | Varies (see docs) |
| **Warmup** | `slowPeriod * 3` bars |
### TL;DR
- DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price...
- Parameterized by `period` (default 40).
- Output range: Varies (see docs).
- Requires `slowPeriod * 3` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price while cancelling longer-term trends. Developed by John Ehlers, the indicator is grounded in cycle theory rather than arbitrary period selection, making it a principled alternative to MACD for cycle-aware trading. Bias-corrected EMAs ensure accurate amplitude during warmup.
## Historical Context
lib/cycles/eacp/eacp.md
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# EACP: Ehlers Autocorrelation Periodogram
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `minPeriod` (default 8), `maxPeriod` (default 48), `avgLength` (default 3), `enhance` (default true) |
| **Outputs** | Single series (Eacp) |
| **Output range** | Varies (see docs) |
| **Warmup** | `maxPeriod * 2` bars |
### TL;DR
- EACP estimates the dominant cycle period of a financial time series by computing autocorrelation across multiple lags and transforming the result i...
- Parameterized by `minperiod` (default 8), `maxperiod` (default 48), `avglength` (default 3), `enhance` (default true).
- Output range: Varies (see docs).
- Requires `maxPeriod * 2` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
EACP estimates the dominant cycle period of a financial time series by computing autocorrelation across multiple lags and transforming the result into a power spectrum via the Wiener-Khinchin theorem. The output is a continuously updating cycle period measurement (in bars) that can adaptively tune other indicators to the market's current rhythm, making fixed-period assumptions unnecessary.
## Historical Context
lib/cycles/ebsw/ebsw.md
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# EBSW: Ehlers Even Better Sinewave
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `hpLength` (default 40), `ssfLength` (default 10) |
| **Outputs** | Single series (Ebsw) |
| **Output range** | Varies (see docs) |
| **Warmup** | 1 bar |
### TL;DR
- EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Co...
- Parameterized by `hplength` (default 40), `ssflength` (default 10).
- Output range: Varies (see docs).
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Control to produce a normalized $[-1, +1]$ output representing the current position within the dominant market cycle. Developed by John Ehlers as an improvement over the original Hilbert Transform SineWave, it provides cleaner turning point detection without requiring complex phase extraction mathematics.
## Historical Context
lib/cycles/homod/homod.md
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# HOMOD: Ehlers Homodyne Discriminator
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `minPeriod` (default 6.0), `maxPeriod` (default 50.0) |
| **Outputs** | Single series (Homod) |
| **Output range** | Varies (see docs) |
| **Warmup** | 1 bar |
### TL;DR
- HOMOD estimates the dominant cycle period of a market using homodyne mixing, a technique from radio engineering where a signal is multiplied by a d...
- Parameterized by `minperiod` (default 6.0), `maxperiod` (default 50.0).
- Output range: Varies (see docs).
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
HOMOD estimates the dominant cycle period of a market using homodyne mixing, a technique from radio engineering where a signal is multiplied by a delayed copy of itself to expose the angular phase change between samples. The output is a continuously varying period measurement (in bars) that tracks the market's instantaneous cycle length, enabling adaptive indicator tuning. Developed by John Ehlers, it offers better noise rejection and stability than the raw Hilbert Transform period estimator.
## Historical Context
lib/cycles/ht_dcperiod/HtDcperiod.md
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# HT_DCPERIOD: Ehlers Hilbert Transform Dominant Cycle Period
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (HT_DCPERIOD) |
| **Output range** | Varies (see docs) |
| **Warmup** | `LOOKBACK` bars |
### TL;DR
- HT_DCPERIOD estimates the period of the dominant market cycle using Ehlers' Hilbert Transform cascade.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
HT_DCPERIOD estimates the period of the dominant market cycle using Ehlers' Hilbert Transform cascade. The algorithm extracts In-Phase and Quadrature components from price, computes instantaneous phase via homodyne discrimination, and derives the period from the phase rate of change. Output is a continuously varying period (typically 6-50 bars) compatible with TA-Lib's `HT_DCPERIOD` function. The indicator enables dynamic tuning of other indicators to the market's actual rhythm rather than fixed-parameter assumptions.
## Historical Context
lib/cycles/ht_dcphase/HtDcphase.md
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# HT_DCPHASE: Ehlers Hilbert Transform Dominant Cycle Phase
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (HT_DCPHASE) |
| **Output range** | Varies (see docs) |
| **Warmup** | `LOOKBACK` bars |
### TL;DR
- HT_DCPHASE measures the instantaneous phase angle of the dominant market cycle using Ehlers' Hilbert Transform cascade.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
HT_DCPHASE measures the instantaneous phase angle of the dominant market cycle using Ehlers' Hilbert Transform cascade. The output ranges from $-45°$ to $315°$, with phase discontinuities at cycle completions marking the transition from one cycle to the next. Compatible with TA-Lib's `HT_DCPHASE` function, the indicator enables cycle-position timing for entries and exits based on where price currently sits within the dominant cycle.
## Historical Context
lib/cycles/ht_phasor/HtPhasor.md
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# HT_PHASOR: Ehlers Hilbert Transform Phasor Components
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (HT_PHASOR) |
| **Output range** | Varies (see docs) |
| **Warmup** | `LOOKBACK` bars |
### TL;DR
- HT_PHASOR decomposes the price signal into two orthogonal components, InPhase ($I$) and Quadrature ($Q$), using the Hilbert Transform.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
HT_PHASOR decomposes the price signal into two orthogonal components, InPhase ($I$) and Quadrature ($Q$), using the Hilbert Transform. Together these form a complex phasor $Z = I + jQ$ that describes the instantaneous amplitude and phase of the dominant market cycle. Compatible with TA-Lib's `HT_PHASOR` function, this dual-output indicator provides the fundamental building blocks for cycle analysis, phasor crossover timing, and instantaneous amplitude measurement.
## Historical Context
lib/cycles/ht_sine/HtSine.md
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# HT_SINE: Ehlers Hilbert Transform SineWave (also known as SINE)
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (HT_SINE) |
| **Output range** | Varies (see docs) |
| **Warmup** | `LOOKBACK` bars |
### TL;DR
- HT_SINE extracts the dominant market cycle phase and outputs both Sine and LeadSine (45° phase advance) for cycle timing.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
HT_SINE extracts the dominant market cycle phase and outputs both Sine and LeadSine (45° phase advance) for cycle timing. The crossover of these two waves identifies turning points in ranging markets up to one-eighth of a cycle early. Compatible with TA-Lib's `HT_SINE` function, the indicator builds on the full Hilbert Transform cascade (phasor extraction, homodyne period estimation, DFT phase accumulation) to produce dual bounded $[-1, +1]$ oscillators that track cycle position rather than price amplitude.
## Historical Context
lib/cycles/lunar/Lunar.md
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# LUNAR: Lunar Phase Indicator
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (LUNAR) |
| **Output range** | Varies (see docs) |
| **Warmup** | `0` bars |
### TL;DR
- LUNAR calculates the Moon's illumination fraction using precise orbital mechanics from Jean Meeus' *Astronomical Algorithms*.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `0` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
LUNAR calculates the Moon's illumination fraction using precise orbital mechanics from Jean Meeus' *Astronomical Algorithms*. Output ranges from 0.0 (New Moon) through 0.5 (Quarter) to 1.0 (Full Moon), providing a continuous astronomical cycle for research into potential lunar-correlated market behavior. The indicator is purely time-based, requires no price data, and has zero warmup since the calculation is deterministic from any timestamp.
## Historical Context
lib/cycles/solar/Solar.md
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# SOLAR: Solar Cycle Indicator
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | None |
| **Outputs** | Single series (SOLAR) |
| **Output range** | Varies (see docs) |
| **Warmup** | `0` bars |
### TL;DR
- SOLAR models Earth's seasonal position relative to the Sun using astronomical ephemeris calculations.
- No configurable parameters; computation is stateless per bar.
- Output range: Varies (see docs).
- Requires `0` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
SOLAR models Earth's seasonal position relative to the Sun using astronomical ephemeris calculations. Output oscillates continuously from $-1.0$ (Winter Solstice) through $0.0$ (Equinoxes) to $+1.0$ (Summer Solstice), providing a smooth, mathematically precise seasonal phase for econometric modeling. Like LUNAR, the indicator is purely time-based, requires no price data, and has zero warmup since the calculation is deterministic from any timestamp.
## Historical Context
lib/cycles/ssfdsp/Ssfdsp.md
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# SSFDSP: Ehlers SSF Detrended Synthetic Price
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Cycle |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 40) |
| **Outputs** | Single series (SsfDsp) |
| **Output range** | Varies (see docs) |
| **Warmup** | `slowPeriod * 2` bars |
### TL;DR
- SSFDSP isolates the dominant cycle by subtracting a half-cycle Super-Smoother from a quarter-cycle Super-Smoother, producing a zero-centered oscill...
- Parameterized by `period` (default 40).
- Output range: Varies (see docs).
- Requires `slowPeriod * 2` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
SSFDSP isolates the dominant cycle by subtracting a half-cycle Super-Smoother from a quarter-cycle Super-Smoother, producing a zero-centered oscillator with superior noise rejection compared to the EMA-based DSP. The 2-pole Butterworth characteristic of the Super-Smoother filter provides zero phase lag at the cutoff frequency and sharper rolloff than exponential smoothing, making SSFDSP the preferred variant for cycle-aware trading when the approximate dominant period is known.
## Historical Context