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Merge branch 'dev'
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Miha Kralj
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| **PineScript** | [ccor.pine](ccor.pine) |
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- CCOR extracts cycle phase by computing Pearson correlation of a price window against cosine (Real) and negative-sine (Imaginary) reference waves of...
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- Parameterized by `period` (default 20), `threshold` (default 9.0).
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- Output range: Varies (see docs).
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [Ccyc](../ccyc/Ccyc.md), [CG](../cg/cg.md) | **Complementary:** Hilbert Transform for phase analysis | **Trading note:** Cycle correlation; detects dominant cycle period in price data.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -136,4 +134,4 @@ For default period $N = 20$: ~269 cycles per bar. The O(N) cost comes from dual
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- **Ehlers, J.F.** "Correlation As A Cycle Indicator." *Technical Analysis of Stocks & Commodities*, June 2020.
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001. (Hilbert Transform phasor predecessor)
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004. (Broader cycle analysis framework)
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- **Pearson, K.** "Notes on Regression and Inheritance in the Case of Two Parents." *Proceedings of the Royal Society of London*, 58, 1895. (Original Pearson correlation)
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- **Pearson, K.** "Notes on Regression and Inheritance in the Case of Two Parents." *Proceedings of the Royal Society of London*, 58, 1895. (Original Pearson correlation)
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| **PineScript** | [ccyc.pine](ccyc.pine) |
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- 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 ...
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- Parameterized by `alpha` (default 0.07).
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- Output range: Varies (see docs).
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- Requires `7` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [Ccor](../ccor/Ccor.md), [CG](../cg/cg.md) | **Complementary:** EBSW for trend/cycle mode | **Trading note:** Cyber Cycle; Ehlers' bandpass approach to isolate dominant market cycles.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -152,4 +150,4 @@ O(1) per bar. The 4-tap FIR smoother uses 3 MUL + 2 ADD; the 2-pole IIR high-pas
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001. (Foundational DSP framework for markets)
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- **Ehlers, J.F.** "Cybernetic Analysis." *Technical Analysis of Stocks & Commodities*, 2004.
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- **Wiener, N.** *Cybernetics: Or Control and Communication in the Animal and the Machine*. MIT Press, 1948. (Origin of the "cybernetic" terminology)
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- **Oppenheim, A.V. & Schafer, R.W.** *Discrete-Time Signal Processing*. Pearson, 2009. (IIR filter theory, z-domain analysis)
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- **Oppenheim, A.V. & Schafer, R.W.** *Discrete-Time Signal Processing*. Pearson, 2009. (IIR filter theory, z-domain analysis)
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+1
-3
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| **PineScript** | [cg.pine](cg.pine) |
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- CG identifies potential turning points using the physics concept of weighted center of mass applied to a price window.
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- Parameterized by `period` (default 10).
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- Output range: Varies (see docs).
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [Ccyc](../ccyc/Ccyc.md), [EACP](../eacp/eacp.md) | **Complementary:** RSI for momentum confirmation | **Trading note:** Center of Gravity oscillator by Ehlers; leads price turns with minimal lag.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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| **PineScript** | [dsp.pine](dsp.pine) |
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- DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price...
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- Parameterized by `period` (default 40).
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- Output range: Varies (see docs).
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- Requires `slowPeriod * 3` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [SSFDSP](../ssfdsp/Ssfdsp.md), [Ccyc](../ccyc/Ccyc.md) | **Complementary:** ATR for volatility filter | **Trading note:** Digital Signal Processing filter; separates signal from noise in price data.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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| **PineScript** | [eacp.pine](eacp.pine) |
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- EACP estimates the dominant cycle period of a financial time series by computing autocorrelation across multiple lags and transforming the result i...
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- Parameterized by `minperiod` (default 8), `maxperiod` (default 48), `avglength` (default 3), `enhance` (default true).
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- Output range: Varies (see docs).
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- Requires `maxPeriod * 2` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [CG](../cg/cg.md), [HT_DCPeriod](../ht_dcperiod/ht_dcperiod.md) | **Complementary:** EBSW for trend/cycle classification | **Trading note:** Ehlers Autocorrelation Periodogram; identifies dominant cycle length adaptively.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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| **PineScript** | [ebsw.pine](ebsw.pine) |
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- EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Co...
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- Parameterized by `hplength` (default 40), `ssflength` (default 10).
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- Output range: Varies (see docs).
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- Requires `Math.Max(hpLength, ssfLength) + 3` bars (default 43) of warmup before first valid output (IsHot = true).
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- **Similar:** [HT_TrendMode](../../dynamics/ht_trendmode/ht_trendmode.md), [VHF](../../dynamics/vhf/Vhf.md) | **Complementary:** ADX for trend strength | **Trading note:** Even Better Sine Wave; classifies market as trending or cycling.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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| **PineScript** | [homod.pine](homod.pine) |
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- 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...
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- Parameterized by `minperiod` (default 6.0), `maxperiod` (default 50.0).
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- Output range: Varies (see docs).
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- Requires `maxPeriod * 2` bars (default 100) of warmup before first valid output (IsHot = true).
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- **Similar:** [HT_Phasor](../ht_phasor/ht_phasor.md), [HT_Sine](../ht_sine/ht_sine.md) | **Complementary:** Cycle period for context | **Trading note:** Homodyne discriminator; Ehlers' phase detection for cycle turning points.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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- HT_DCPERIOD estimates the period of the dominant market cycle using Ehlers' Hilbert Transform cascade.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -112,4 +110,4 @@ The period range [6, 50] and all smoothing constants are fixed by the TA-Lib spe
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001.
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- **TA-Lib** `TA_HT_DCPERIOD()` reference implementation.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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@@ -14,8 +14,6 @@
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- HT_DCPHASE measures the instantaneous phase angle of the dominant market cycle using Ehlers' Hilbert Transform cascade.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -114,4 +112,4 @@ All internal constants are fixed by the TA-Lib specification.
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001.
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- **TA-Lib** `TA_HT_DCPHASE()` reference implementation.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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- **Hilbert, D.** *Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen*. Teubner, 1912.
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- **Hilbert, D.** *Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen*. Teubner, 1912.
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@@ -14,8 +14,6 @@
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- HT_PHASOR decomposes the price signal into two orthogonal components, InPhase ($I$) and Quadrature ($Q$), using the Hilbert Transform.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -105,4 +103,4 @@ $O(1)$ per bar. Fixed Hilbert cascade with circular buffers. Warmup: 32 bars (TA
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001.
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- **TA-Lib** `TA_HT_PHASOR()` reference implementation.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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@@ -14,8 +14,6 @@
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- HT_SINE extracts the dominant market cycle phase and outputs both Sine and LeadSine (45° phase advance) for cycle timing.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `LOOKBACK` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -119,4 +117,4 @@ All constants are fixed by the TA-Lib specification.
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- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001.
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- **TA-Lib** `TA_HT_SINE()` reference implementation.
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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- **Hilbert, D.** *Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen*. Teubner, 1912.
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- **Hilbert, D.** *Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen*. Teubner, 1912.
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@@ -14,8 +14,6 @@
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- LUNAR calculates the Moon's illumination fraction using precise orbital mechanics from Jean Meeus' *Astronomical Algorithms*.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -126,4 +124,4 @@ The calculation is entirely determined by the input timestamp.
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- **Meeus, J.** *Astronomical Algorithms*. 2nd ed., Willmann-Bell, 1998.
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- **Dichev, I.D. & Janes, T.D.** "Lunar Cycle Effects in Stock Returns." *Journal of Private Equity*, 2001.
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- **Yuan, K., Zheng, L. & Zhu, Q.** "Are Investors Moonstruck? Lunar Phases and Stock Returns." *Journal of Empirical Finance*, 2006.
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- **Yuan, K., Zheng, L. & Zhu, Q.** "Are Investors Moonstruck? Lunar Phases and Stock Returns." *Journal of Empirical Finance*, 2006.
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@@ -14,8 +14,6 @@
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- SOLAR models Earth's seasonal position relative to the Sun using astronomical ephemeris calculations.
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- No configurable parameters; computation is stateless per bar.
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- Output range: Varies (see docs).
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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## Resources
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- **Meeus, J.** *Astronomical Algorithms*. 2nd ed., Willmann-Bell, 1998.
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- **USNO** *Astronomical Almanac*. U.S. Government Publishing Office (annual reference for solstice/equinox verification).
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- **USNO** *Astronomical Almanac*. U.S. Government Publishing Office (annual reference for solstice/equinox verification).
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@@ -13,9 +13,7 @@
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| **PineScript** | [ssfdsp.pine](ssfdsp.pine) |
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- SSFDSP isolates the dominant cycle by subtracting a half-cycle Super-Smoother from a quarter-cycle Super-Smoother, producing a zero-centered oscill...
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- Parameterized by `period` (default 40).
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- Output range: Varies (see docs).
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- Requires `slowPeriod * 2` bars of warmup before first valid output (IsHot = true).
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- **Similar:** [DSP](../dsp/dsp.md), [SSF2](../../filters/ssf2/Ssf2.md) | **Complementary:** Roofing filter for preprocessing | **Trading note:** Super Smoother with DSP; combines Ehlers' smoothing with signal processing.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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@@ -119,4 +117,4 @@ The SSF has $-3$ dB attenuation at the cutoff period, $-12$ dB/octave rolloff (2
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- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
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- **Ehlers, J.F.** *Cycle Analytics for Traders*. Wiley, 2013.
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- **Butterworth, S.** "On the Theory of Filter Amplifiers." *Experimental Wireless*, 7, 1930.
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- **Butterworth, S.** "On the Theory of Filter Amplifiers." *Experimental Wireless*, 7, 1930.
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