mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-15 00:58:04 +00:00
99 lines
4.7 KiB
Markdown
99 lines
4.7 KiB
Markdown
# 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](dwma.pine) |
|
||
| **Signature** | [dwma_signature](dwma_signature.md) |
|
||
|
||
- DWMA (Double Weighted Moving Average) is exactly what it says on the tin: a Weighted Moving Average of a Weighted Moving Average.
|
||
- **Similar:** [WMA](../wma/wma.md), [FWMA](../fwma/fwma.md) | **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. |