QuanTAlib/lib/trends_FIR/dwma/Dwma.md

DWMA: Double Weighted Moving Average

If one WMA is good, two must be better. DWMA is for when you want your signal so smooth it looks like it's been sanded, polished, and waxed.

Property	Value
Category	Trend (FIR MA)
Inputs	Source (close)
Parameters	period
Outputs	Single series (Dwma)
Output range	Tracks input
Warmup	(period * 2) - 1 bars
PineScript	dwma.pine
Signature	dwma_signature

• DWMA (Double Weighted Moving Average) is exactly what it says on the tin: a Weighted Moving Average of a Weighted Moving Average.
• Similar: WMA, FWMA | Complementary: Volume confirmation | Trading note: Distance-Weighted MA; assigns weights based on distance from current bar.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

DWMA (Double Weighted Moving Average) is exactly what it says on the tin: a Weighted Moving Average of a Weighted Moving Average. Unlike DEMA, which tries to remove lag, DWMA accepts lag as the price of admission for superior noise reduction. It produces a curve that is incredibly smooth, ideal for identifying long-term trends without getting faked out by market chop.

Historical Context

There is no single "inventor" of DWMA; it's a natural extension of linear filtering. It represents a higher-order filter that prioritizes recent data (via WMA) but applies a second pass to iron out any remaining wrinkles. It's the heavy artillery of smoothing.

Architecture & Physics

DWMA applies a linear weight kernel (triangle window) twice.

1. Pass 1: Calculate WMA of the price.
2. Pass 2: Calculate WMA of the result from Pass 1.

The effective window size is roughly 2 \times \text{Period}, and the lag is cumulative. This is not for high-frequency scalping; this is for determining if the market is actually bullish or just having a manic episode.

Mathematical Foundation

\text{WMA}_1 = \text{WMA}(P, N) \text{DWMA} = \text{WMA}(\text{WMA}_1, N)

The weight profile of a single WMA is triangular. The weight profile of a DWMA approaches a Gaussian-like shape (central limit theorem in action), but heavily skewed towards recent data due to the WMA's linear weighting.

Performance Profile

Operation Count (Streaming Mode, Scalar)

DWMA chains two WMA instances. Each WMA is O(1) with ~22 cycles (see WMA.md).

Component	Operations	Cost (cycles)
WMA₁(Price)	4 ADD/SUB, 1 MUL, 1 DIV	~22
WMA₂(WMA₁)	4 ADD/SUB, 1 MUL, 1 DIV	~22
Total	8 ADD/SUB, 2 MUL, 2 DIV	~44 cycles

Hot path breakdown:

• First WMA smooths the raw price → ~22 cycles
• Second WMA smooths the first WMA's output → ~22 cycles
• No additional combining math required

Batch Mode (SIMD)

Each WMA component benefits from SIMD prefix-sum optimization:

Component	Scalar (512 bars)	SIMD (AVX2)	Speedup
WMA₁ prefix sum	~11K cycles	~2.8K cycles	~4×
WMA₂ prefix sum	~11K cycles	~2.8K cycles	~4×
Total	~22K	~5.6K	~4×

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Matches chained WMA exactly
Timeliness	3/10	Significant lag; double smoothing delays signals
Overshoot	10/10	Never overshoots input data range (FIR property)
Smoothness	9/10	Very smooth; approaches Gaussian-like profile

Zero-Allocation Design

DWMA is implemented by chaining two Wma instances. Since Wma is zero-allocation, DWMA inherits this property.

Validation

Validated against chained WMA implementations in standard libraries.

Library	Status	Notes
QuanTAlib	✅	Validated against WMA(WMA).
Skender	✅	Validated against chained GetWma.
TA-Lib	✅	Validated against chained TA_WMA.
Tulip	✅	Validated against chained wma.
Ooples	✅	Validated against chained CalculateWeightedMovingAverage.

Common Pitfalls

1. Lag: This indicator lags. A lot. Do not use it for entry signals on tight timeframes. Use it for trend filtering (e.g., "only buy if price > DWMA").
2. Warmup: It takes roughly 2 \times N bars to produce valid data.
3. Confusion with DEMA: DEMA = Fast, DWMA = Smooth. Do not mix them up.