QuanTAlib/lib/cycles/_index.md

Cycles

"The market is a discounting mechanism that anticipates cycles before they complete."  Unknown

Cycle analysis identifies repeating patterns in price data. John Ehlers pioneered digital signal processing techniques for financial cycles, using Hilbert transforms and autocorrelation to detect dominant periods. Cycles exist but are non-stationary: period and amplitude shift over time.

Indicator Status

Indicator	Full Name	Status	Description
CFB	Composite Fractal Behavior	=�	Jurik's fractal-based cycle detection. Adapts to changing volatility.
CG	Center of Gravity	=�	Ehlers. Weighted sum position. Minimal lag cycle indicator.
DSP	Detrended Synthetic Price	=�	Removes trend to reveal underlying cycles.
EACP	Autocorrelation Periodogram	=�	Ehlers. Spectral analysis via autocorrelation. Detects dominant period.
EBSW	Even Better Sinewave	=�	Ehlers. Improved sinewave extraction. Reduces false signals.
SSFDSP	SSF Detrended Synthetic Price	=�	Super Smoother Filter based DSP. Cleaner cycle extraction.
HOMOD	Homodyne Discriminator	=�	Dominant cycle detection via homodyne technique.
HT_DCPERIOD	HT Dominant Cycle Period	=�	Ehlers Hilbert Transform. Measures current cycle length.
HT_DCPHASE	HT Dominant Cycle Phase	=�	Ehlers Hilbert Transform. Measures current position in cycle.
HT_PHASOR	HT Phasor Components	=�	Ehlers. In-phase and quadrature components.
HT_SINE	HT SineWave	=�	Ehlers. Sine and lead sine for cycle timing.
LUNAR	Lunar Phase	=�	29.5-day lunar cycle. Studied for market correlations.
PHASOR	Phasor Analysis	=�	Ehlers. Phase angle from Hilbert Transform.
SINE	Sine Wave	=�	Ehlers. Basic sinewave indicator for cycle mode.
SOLAR	Solar Activity Cycle	=�	~11-year sunspot cycle. Long-term research indicator.
STC	Schaff Trend Cycle		MACD + double Stochastic smoothing. Fast cycle oscillator (0-100).

Status Key:  Implemented | =� Planned

Selection Guide

Use Case	Recommended	Why
Dominant cycle detection	EACP, HT_DCPERIOD	Spectral analysis identifies strongest periodic component.
Cycle timing	HT_SINE, EBSW	Sine/lead-sine crossovers signal cycle turns.
Trend + cycle hybrid	STC	Combines MACD trend with Stochastic cycle. Fast signals.
Minimal lag	CG	Center of Gravity has theoretical zero lag at cycle frequency.
Phase analysis	HT_PHASOR, PHASOR	Track position within current cycle.

Ehlers Cycle Framework

John Ehlers developed most modern cycle indicators using DSP principles:

Component	Purpose	Implementation
Hilbert Transform	Extracts instantaneous phase	90� phase shift via FIR filter
Super Smoother	Pre-filter noise	2-pole Butterworth variant
Homodyne	Period detection	Multiplies signal by delayed version
Autocorrelation	Spectral density	Correlates signal with lagged self

Key insight: Financial cycles are non-stationary. Fixed-period indicators fail. Adaptive techniques (EACP, HT_DCPERIOD) measure the current dominant period and adjust accordingly.

Cycle vs Trend

Market Condition	Use Cycles	Use Trends
Ranging/choppy	 Cycles excel	L Whipsaws
Strong trend	L False signals	 Trend-following works
Transition periods	� Regime detection	� Lag at turns

Combine cycle indicators with trend filters. Trade cycles only when trend strength is low.