QuanTAlib/lib/trends_IIR/mgdi/Mgdi.md

MGDI: McGinley Dynamic Indicator

John McGinley saw moving averages failing in fast markets and said, 'It's not the market's fault, it's the math's fault.' MGDI is the apology.

Property	Value
Category	Trend (IIR MA)
Inputs	Source (close)
Parameters	period (default 14), k (default 0.6)
Outputs	Single series (Mgdi)
Output range	Tracks input
Warmup	period bars
PineScript	mgdi.pine
Signature	mgdi_signature

• MGDI (McGinley Dynamic Indicator) looks like a moving average but operates on a fundamentally different principle.
• Similar: JMA, KAMA | Complementary: Momentum oscillators | Trading note: McGinley Dynamic; self-adjusts to market speed.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

MGDI (McGinley Dynamic Indicator) looks like a moving average but operates on a fundamentally different principle. Rather than using a fixed smoothing factor, it dynamically adjusts based on the ratio between price and the indicator's current value. The result is a filter that accelerates to catch breakouts while decelerating to avoid overshooting reversals—a behavior that fixed-alpha filters cannot achieve.

Historical Context

Published by John McGinley in the Market Technicians Association Journal (1991), the Dynamic was created to be a "market tool" rather than just an indicator. McGinley observed that traditional moving averages have a fundamental flaw: their fixed period means they're either too slow in fast markets or too jittery in slow ones.

His insight was that the appropriate smoothing should depend on the relationship between price and the average itself. When price pulls far ahead, the average should accelerate. When price falls back toward the average, it should decelerate to avoid overshooting. The fourth-power ratio term creates this asymmetric, self-correcting behavior.

Architecture & Physics

MGDI uses a nonlinear feedback mechanism that creates adaptive smoothing.

1. The Core Recursion

The update formula resembles an EMA but with a dynamic denominator:

\text{MGDI}_t = \text{MGDI}_{t-1} + \frac{P_t - \text{MGDI}_{t-1}}{k \times N \times \left(\frac{P_t}{\text{MGDI}_{t-1}}\right)^4}

The numerator (P_t - \text{MGDI}_{t-1}) is the standard "error" term—how far price is from the current estimate.

2. The Adaptive Denominator

The denominator k \times N \times (P_t / \text{MGDI}_{t-1})^4 is where the magic happens:

• When $P_t > \text{MGDI}_{t-1}$: The ratio exceeds 1, the fourth power amplifies it, the denominator grows, and the adjustment shrinks. This prevents overshooting during rallies.

• When $P_t < \text{MGDI}_{t-1}$: The ratio is below 1, the fourth power shrinks it further, the denominator shrinks, and the adjustment grows. This allows faster catch-up during declines.

3. The Fourth Power Effect

The exponent of 4 creates strong nonlinearity:

P_t / \text{MGDI}_{t-1}	(P_t / \text{MGDI}_{t-1})^4	Effect
1.10	1.46	Moderate slowdown
1.20	2.07	Significant slowdown
0.95	0.81	Mild speedup
0.90	0.66	Aggressive speedup

This asymmetry is intentional: rallies are allowed to "run" without the indicator overshooting, while declines are tracked more aggressively.

Mathematical Foundation

The Update Formula

\text{MGDI}_t = \text{MGDI}_{t-1} + \frac{P_t - \text{MGDI}_{t-1}}{k \times N \times \left(\frac{P_t}{\text{MGDI}_{t-1}}\right)^4}

Where:

• N is the period (calibration parameter, not a lookback window)
• k is the McGinley constant (standard value: 0.6)
• P_t is the current price
• \text{MGDI}_{t-1} is the previous indicator value

Effective Alpha

The effective smoothing factor varies with each bar:

\alpha_{eff} = \frac{1}{k \times N \times \left(\frac{P_t}{\text{MGDI}_{t-1}}\right)^4}

For N=14 and k=0.6, the effective alpha ranges from approximately 0.05 to 0.20 depending on price/indicator ratio.

Relationship to EMA

When P_t = \text{MGDI}_{t-1} (price equals indicator):

\alpha_{eff} = \frac{1}{k \times N} = \frac{1}{0.6 \times N}

For N=14: \alpha_{eff} = 0.119, which corresponds to roughly EMA(16).

Initialization

The first value is typically set to the first price: \text{MGDI}_0 = P_0.

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Cost (cycles)	Subtotal
DIV	1	15	15
POW (x^4)	1	~12	12
MUL	2	3	6
ADD/SUB	2	1	2
Total	6	—	~35 cycles

The fourth power can be computed as two squarings: (x^2)^2, avoiding the expensive Math.Pow call.

Batch Mode (SIMD/FMA Analysis)

MGDI is inherently recursive (each value depends on the previous), limiting SIMD parallelization. However, optimizations include:

Optimization	Benefit
Inline squaring vs Math.Pow	~20 cycles saved
FMA for numerator calc	~2 cycles saved
Precompute k \times N	Constant folding

Effective throughput: ~30 cycles/bar after optimization.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	Hugs price closely without breaking
Timeliness	8/10	Accelerates to catch up to price
Overshoot	9/10	Specifically designed to minimize overshoot
Smoothness	9/10	Visually pleasing, organic curve

Benchmark Results

Metric	Value	Notes
Throughput	~8 ns/bar	Division and power dominate
Allocations	0 bytes	Stack-based calculations only
Complexity	O(1)	Constant time update
State Size	16 bytes	Single double + flags

Benchmarked on Intel i7-12700K @ 3.6 GHz, AVX2, .NET 10.0

Validation

Library	Status	Notes
Skender	✅	Matches GetDynamic (tolerance: 1e-9)
Ooples	✅	Matches CalculateMcGinleyDynamicIndicator
TA-Lib	N/A	Not implemented
Tulip	N/A	Not implemented

Common Pitfalls

1. Not an EMA: MGDI does not have a fixed alpha. Period comparisons with EMA are approximate at best. MGDI(14) does not equal EMA(14) in behavior or lag characteristics.

2. Period Is Calibration: The "Period" N is a calibration constant, not a lookback window. MGDI(14) doesn't examine 14 bars of history—it's tuned to track instruments that typically move in 14-bar cycles.

3. K Factor Sensitivity: The constant k=0.6 is McGinley's recommended value. Reducing it (e.g., 0.4) makes the indicator more responsive but increases overshoot risk. Increasing it (e.g., 0.8) smooths further but adds lag.

4. Division by Zero: If \text{MGDI}_{t-1} = 0 (only possible with zero or negative prices), the formula fails. Implementation must guard against this edge case.

5. Warmup Behavior: The first few bars can exhibit unusual behavior until the indicator "locks on" to the price series. Allow 5-10 bars for stabilization.

6. Ratio Extremes: In volatile markets, the ratio P_t / \text{MGDI}_{t-1} can reach extreme values. Some implementations clamp this ratio to prevent numerical instability.

7. Bar Correction: Use isNew=false for same-bar updates. The nonlinear formula means small price changes can produce disproportionate output changes during bar formation.

References

• McGinley, J.R. (1991). "The McGinley Dynamic." Market Technicians Association Journal, Fall 1991.