QuanTAlib/lib/trends_IIR/_index.md

Trends (IIR)

"Recursion trades memory for computation. Single coefficient replaces entire window. But feedback loop carries risk: instability lurks in coefficient choices that FIR designers never face."

Trend indicators based on Infinite Impulse Response (IIR) filters. Recursive architecture uses previous outputs to compute current values, enabling lower lag with fewer coefficients than equivalent FIR filters.

Implementation Status

Indicator	Full Name	Status	Description
DEMA	Double Exponential MA		Reduces lag by applying double exponential smoothing, enhancing responsiveness while maintaining signal quality.
DSMA	Deviation-Scaled MA		Adaptive IIR filter that adjusts smoothing factor based on market volatility, increasing responsiveness during high-deviation periods.
EMA	Exponential MA		Applies exponentially decreasing weights to price data, balancing responsiveness and stability.
FRAMA	Fractal Adaptive MA		Adapts smoothing based on fractal dimension analysis, minimizing lag in trends and maximizing smoothing in consolidation.
HEMA	Hull Exponential MA		EMA-domain Hull analog using half-life timing and de-lagged EMA cascade.
HTIT	Hilbert Transform Instantaneous Trend		Utilizes Hilbert Transform to isolate instantaneous trend component, providing zero-lag trendline with hybrid FIR-in-IIR design.
JMA	Jurik MA		Adaptive filter achieving high noise reduction and low phase delay through multi-stage volatility normalization and dynamic parameter optimization.
KAMA	Kaufman Adaptive MA		Automatically adjusts sensitivity based on market volatility using Efficiency Ratio, balancing responsiveness and stability.
MAMA	MESA Adaptive MA		Applies Hilbert Transform for phase-based adaptation, using dual-line system (MAMA/FAMA) for cycle-sensitive smoothing.
MGDI	McGinley Dynamic Indicator		Adjusts speed based on market volatility using dynamic factor, aiming to hug prices closely.
MMA	Modified MA		Combines simple and weighted components, emphasizing central values for balanced smoothing.
QEMA	Quad Exponential MA		Zero-lag filter with four cascaded EMAs using geometrically ramped alphas and minimum-energy weights for DC lag elimination.
REMA	Regularized Exponential MA		Applies regularization to EMA using lambda parameter, balancing smoothing and momentum-based prediction.
RGMA	Recursive Gaussian MA		Approximates Gaussian smoothing by recursively applying EMA filters multiple times (passes), controlled by adjusted period.
RMA	wildeR MA (SMMA, MMA)		Wilder's smoothing average using specific alpha (1/period), designed for indicators like RSI and ATR.
T3	Tillson T3 MA		Six-stage EMA cascade with optimized coefficients based on volume factor for reduced lag and superior noise reduction.
TEMA	Triple Exponential MA		Triple-cascade EMA architecture with optimized coefficients (3, -3, 1) for further lag reduction compared to DEMA.
VAMA	Volatility Adjusted MA		Dynamically adjusts moving average length based on ATR volatility ratio, shortening during high volatility and lengthening during low volatility.
VIDYA	Variable Index Dynamic Average		Adjusts smoothing factor based on market volatility using Volatility Index (ratio of short-term to long-term standard deviation).
YZVAMA	Yang-Zhang Volatility Adjusted MA		Adjusts MA length based on percentile rank of short-term YZV, providing context-aware volatility adaptation for gap-prone markets.
ZLEMA	Zero-Lag Exponential MA		Reduces lag by estimating future price based on current momentum, using dynamically calculated lag period.

Selection Guide

For trend-following systems: EMA provides baseline stability. DEMA/TEMA reduce lag at cost of increased overshoot. T3 offers best lag-to-smoothness ratio for most applications.

For adaptive response: KAMA adjusts to efficiency ratio (trend vs noise). VIDYA responds to volatility changes. FRAMA uses fractal dimension for market state detection. JMA combines all adaptive mechanisms into unified filter.

For zero-lag requirements: ZLEMA applies momentum-based lag compensation. HTIT uses Hilbert Transform for instantaneous trend. QEMA achieves DC lag elimination through cascaded architecture.

For Wilder-family indicators: RMA (SMMA) provides standard smoothing for RSI, ATR, ADX calculations.

IIR Characteristics Comparison

Filter	Lag (bars)	Smoothness	Overshoot	Adaptivity	Complexity
EMA	Period/2	Medium	Low	None	O(1)
DEMA	Period/3	Medium	Medium	None	O(1)
TEMA	Period/4	Low	High	None	O(1)
T3	Period/5	High	Low	None	O(1)
ZLEMA	~0	Low	High	None	O(1)
KAMA	Variable	Variable	Low	Efficiency	O(n)
VIDYA	Variable	Variable	Low	Volatility	O(n)
FRAMA	Variable	Variable	Medium	Fractal	O(n)
JMA	~1-2	High	Very Low	Multi-factor	O(1)

Adaptive Filter Categories

Category	Filters	Adaptation Mechanism	Best Application
Fixed Alpha	EMA, RMA, MMA	Constant smoothing factor	Stable trending markets
Cascade	DEMA, TEMA, T3, QEMA	Multiple EMA stages	Lag reduction priority
Efficiency-Based	KAMA	Direction vs noise ratio	Choppy/trending detection
Volatility-Based	VIDYA, VAMA, DSMA, YZVAMA	Standard deviation or ATR	Regime-change adaptation
Fractal-Based	FRAMA	Hurst exponent proxy	Range/trend detection
Phase-Based	MAMA, HTIT	Hilbert Transform	Cycle-sensitive smoothing
Multi-Stage Adaptive	JMA, MGDI	Combined mechanisms	Universal application

IIR vs FIR Design Principles

Aspect	IIR Filters	FIR Filters
Memory	O(1) state	O(period) buffer
Computation	2-4 multiplications	period multiplications
Stability	Requires careful design	Always stable
Phase Response	Non-linear phase	Can be linear phase
Lag Achievable	Lower lag possible	Minimum lag = (period-1)/2
Adaptivity	Natural (modify alpha)	Requires coefficient recalc
SIMD Potential	Limited (recursive)	High (parallel windows)

Alpha-Period Relationship

IIR filters use smoothing factor ± instead of explicit period. Conversion formulas:

Formula	Expression	Use Case
Standard EMA	± = 2/(period+1)	General purpose
Wilder (RMA)	± = 1/period	RSI, ATR, ADX
Percentage	± = percentage/100	Direct control

Effective period approximation: period H 2/± - 1 for standard EMA weighting.