QuanTAlib/docs/trendcomparison.md

Trend Indicators Comparison

"All models are wrong, but some are useful." — George Box (and some are less wrong than others)

The tables below present a no-nonsense evaluation of trend-following indicators across four measurable qualities. Higher scores indicate better performance. No indicator achieves 10/10 across all categories. Anyone claiming otherwise is selling something.

The Scorecard

Scale: 1–10 where 10 = better for every column.

IIR Trend Indicators (Recursive / Infinite Impulse Response)

Indicator	Accuracy	Timeliness	Overshoot	Smoothness	Verdict
DEMA	4	9	3	6	Fast but dishonest. Lag cancellation distorts structure.
DSMA	7	8	6	8	Deviation-scaled. Volatility-adaptive with Super Smoother core.
EMA	8	6	10	8	The reliable workhorse. Boring but trustworthy.
FRAMA	8	8	5	7	Fractal adaptive. Adjusts to market roughness via dimension.
HEMA	8	8	6	7	Hull topology with half-life EMA semantics. Fast response.
HTIT	7	8	6	8	Hilbert Transform magic. Works until it doesn't.
JMA	8	9	9	9	The best balance. Proprietary algorithm, reverse-engineered.
KAMA	8	8	10	8	Adaptive alpha. Knows when to sprint, when to coast.
MAMA	6	9	6	3	Phase-adaptive. Fast but accuracy depends on cycle fit.
MGDI	7	7	10	9	McGinley Dynamic. EMA that adjusts speed automatically.
MMA	8	6	4	7	Modified MA. SMA with weighted correction, mild overshoot.
QEMA	9	9	8	8	Quad EMA with optimized weights. Zero-lag on linear trends.
REMA	8	7	3	9	Regularized EMA. Momentum-aware, resists noise-induced whipsaws.
RMA	8	4	10	9	Wilder's smoothing. Stable and patient. Too patient.
T3	7	8	5	10	Triple-smoothed. Beautiful curves, questionable honesty.
TEMA	3	10	3	6	Zero lag illusion. Structure distortion is the price.
VIDYA	10	8	9	7	Chande's variable index. Adapts to volatility via CMO.
ZLEMA	8	8	6	7	Zero-lag via prediction. Pays the price in overshoot.

Additional IIR Indicators (awaiting detailed profiling):

Indicator	Type	Notes
RGMA	Recursive	Regularized Geometric MA
VAMA	Adaptive	Volume-Adaptive MA
YZVAMA	Adaptive	Yang-Zhang Volatility Adaptive MA

FIR Trend Indicators (Finite Impulse Response / Windowed)

Indicator	Accuracy	Timeliness	Overshoot	Smoothness	Verdict
ALMA	8	7	10	8	FIR with Gaussian weights. Solid performer, honest tradeoffs.
BLMA	7	3	10	10	Blackman window. Ultra-smooth but lag dominates.
BWMA	7	4	10	9	Bartlett-Windowed MA. Linear weights, moderate lag.
CONV	7	5	10	7	Generic convolution. Customizable kernel weights.
DWMA	7	2	10	10	Ultra-smooth, ultra-late. Structure gets smeared.
GWMA	10	7	10	9	Centered Gaussian. Optimal smoothing, symmetric weights.
HAMMA	7	4	10	9	Hamming window. Good sidelobe suppression.
HANMA	7	4	10	9	Hanning window. Smooth cosine taper.
HMA	6	9	3	7	Fast and flashy. Overshoots like a nervous trader.
HWMA	7	5	10	8	Holt-Winters MA. Trend + level decomposition.
LSMA	3	8	5	3	Regression endpoint. Extrapolates into fiction.
PWMA	6	7	10	6	Pascal weights. No overshoot, some jitter.
SGMA	8	6	10	8	Savitzky-Golay MA. Polynomial smoothing.
SINEMA	7	5	10	8	Sine-weighted MA. Smooth taper, moderate lag.
SMA	7	3	10	6	The baseline. Everything else compares against this.
TRIMA	7	2	10	10	Triangular weights. Smooth as glass, late as always.
WMA	7	7	10	5	Weighted. Faster than SMA, rougher than EMA.

Signal Processing Filters

Filter	Accuracy	Timeliness	Overshoot	Smoothness	Verdict
BESSEL	9	7	9	8	Preserves waveform shape. Step response behaves predictably.
BILATERAL	7	6	10	8	Edge-preserving. Excels in ranging markets, struggles in trends.
BPF	8	7	7	7	Bandpass filter. Isolates specific frequency bands.
BUTTER	7	7	8	9	Maximally flat passband. Textbook balance of smooth and responsive.
CHEBY1	8	8	6	8	Steeper rolloff than Butter. Passband ripple tradeoff.
CHEBY2	8	8	7	8	Stopband ripple variant. Flat passband, steep cutoff.
ELLIPTIC	8	9	5	7	Sharpest cutoff. Ripple in both bands.
GAUSS	10	8	10	10	FIR Gaussian kernel. No overshoot, optimal smoothing.
HANN	8	6	10	9	Hann window filter. Smooth frequency response.
HP	7	8	6	6	High-pass. Removes DC/trend, passes oscillations.
HPF	7	8	6	6	High-pass filter variant. Trend removal.
KALMAN	10	8	9	9	Optimal recursive estimator. Adapts to noise/signal ratio.
LOESS	9	5	10	9	Local regression. Computationally heavy but accurate.
NOTCH	8	7	8	7	Removes specific frequency. Good for eliminating noise bands.
SGF	9	6	10	9	Savitzky-Golay filter. Polynomial smoothing with derivatives.
SSF	9	8	8	9	Super Smoother. Ehlers' contribution to signal processing.
USF	9	9	8	9	Ultimate Smoother. Lives up to the name, mostly.
WIENER	9	7	9	9	Statistically optimal. Adapts gain to local SNR.

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Reading the Patterns

The Honest Performers (High Accuracy, High Overshoot Control)

EMA, SMA, RMA, KAMA, VIDYA, GWMA, GAUSS

These indicators show what actually happened, even if they show it late. No extrapolation tricks, no lag cancellation gimmicks. They will never overshoot price bounds.

Use when: You need trustworthy signals for threshold-based systems, stop-loss placement, or baseline references.

The Speed Demons (High Timeliness, Low Overshoot Control)

DEMA, TEMA, HMA, MAMA, ELLIPTIC

Fast reaction comes from subtraction/extrapolation techniques that can push the output past where price ever went. They sacrifice accuracy for responsiveness.

Use when: Early detection matters more than precision. Pair with confirmation from honest indicators.

The Smooth Operators (High Smoothness, Low Timeliness)

BLMA, DWMA, TRIMA, T3, GAUSS, LOESS

These filters produce beautiful curves but react to trend changes bars after everyone else. They minimize noise at the cost of responsiveness.

Use when: Long-term trend identification, noise-free visualization, or when you can afford to be late.

The Balanced Contenders (Scores 8+ Across Multiple Columns)

JMA, SSF, USF, BESSEL, QEMA, KALMAN, VIDYA

These represent the current state of the art. Complex algorithms that attempt to break the fundamental lag-vs-smoothness tradeoff. They come closer than most, but physics still wins.

Use when: You need the best available balance and can accept algorithmic complexity.

The Adaptive Family (Dynamic Response)

KAMA, VIDYA, FRAMA, DSMA, MAMA, WIENER, KALMAN

These indicators adjust their behavior based on market conditions—speeding up in trends and slowing down in consolidation.

Use when: Market conditions vary significantly between trending and ranging phases.

The Edge Preservers (Minimal Distortion on Reversals)

BILATERAL, BESSEL, GAUSS, KALMAN

These filters explicitly minimize step response distortion, preserving sharp transitions in the underlying signal.

Use when: Detecting trend reversals without false signals from overshoot.

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The Underlying Physics

For detailed explanation of what each quality measures and why the tradeoffs exist, see Four Core Qualities of Superior Moving Averages.

The short version:

Quality	What It Measures	The Tradeoff
Accuracy	Preservation of true signal structure	Requires seeing enough data (lag)
Timeliness	Speed of response to genuine changes	Fast response includes noise response
Overshoot	Staying within actual price bounds	Lag cancellation causes overshoot
Smoothness	Noise suppression	More smoothing equals more lag

The Fundamental Constraint

No linear filter can simultaneously achieve:

• Zero lag
• Perfect noise suppression
• No overshoot

This is not a software limitation—it's signal processing physics. The Heisenberg-Gabor uncertainty principle for time-frequency analysis guarantees a minimum product of time resolution × frequency resolution. Every indicator choice trades one quality for another.

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Filter Selection Guide

By Use Case

Use Case	Recommended	Avoid
Trend following	JMA, KAMA, VIDYA, SSF	DEMA, TEMA, HMA
Mean reversion	SMA, EMA, GWMA	LSMA, ZLEMA
Volatility bands	EMA, RMA, KALMAN	HMA, DEMA
Signal smoothing	GAUSS, SSF, USF, KALMAN	SMA, WMA
Cycle analysis	SSF, BUTTER, CHEBY1/2	EMA, SMA
Noise removal	GAUSS, BILATERAL, WIENER	WMA, PWMA
Real-time responsiveness	EMA, ZLEMA, QEMA	TRIMA, BLMA, DWMA

By Computational Budget

Budget	Indicators
Minimal (O(1))	EMA, RMA, DEMA, TEMA, ZLEMA, KALMAN
Low (O(1) with state)	JMA, KAMA, VIDYA, FRAMA, SSF, QEMA
Moderate (O(N))	SMA, WMA, ALMA, GWMA, BUTTER
High (O(N²) or more)	LOESS, SGF (high order)

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Test Methodology

All scores derived from standardized tests:

Data: 10,000 bar synthetic series using Geometric Brownian Motion with known drift (0.02% per bar) and volatility (2% annualized).

Accuracy: Correlation between indicator output and the deterministic drift component.

Timeliness: Phase delay measured at the dominant frequency (0.05 cycles/bar).

Overshoot: Maximum excursion beyond input min/max during step response test.

Smoothness: Ratio of output second-derivative variance to input second-derivative variance.

Each indicator tested with parameters normalized to equivalent smoothing bandwidth (10-bar effective lookback).

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References

• Ehlers, J. (2001). "Rocket Science for Traders." Wiley.
• Kaufman, P. (1995). "Smarter Trading." McGraw-Hill.
• Hull, A. (2005). "Hull Moving Average." alanhull.com.
• Jurik, M. (1998). "Jurik Moving Average." Jurik Research.
• Chande, T. (1992). "Variable Index Dynamic Average." TASC.
• Kalman, R.E. (1960). "A New Approach to Linear Filtering." Trans. ASME.
• Wiener, N. (1949). "Extrapolation, Interpolation, and Smoothing of Stationary Time Series." MIT Press.
• Savitzky, A. & Golay, M. (1964). "Smoothing and Differentiation of Data." Analytical Chemistry.