mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
c034cbd5e5
- Introduced YZV class for calculating Yang-Zhang Volatility, a comprehensive volatility measure that incorporates overnight, open-to-close, and high-low components. - Implemented calculation methods, including batch processing for TBarSeries and spans. - Added documentation for YZV, detailing its mathematical foundation, performance profile, and trading applications. - Updated volume index documentation to reflect changes in file paths. - Refactored VWMA calculation method to use a more generic source parameter instead of price.
149 lines
4.8 KiB
Markdown
149 lines
4.8 KiB
Markdown
# ZLDEMA: Zero-Lag Double Exponential Moving Average
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## DEMA with lag compensation via a zero-lag signal
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> "ZLDEMA combines the speed of zero-lag prediction with the smoothness of double exponential averaging. You get faster response than ZLEMA, with better trend-following than DEMA."
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ZLDEMA takes a standard DEMA and feeds it a **zero-lag signal**: current price minus a lagged price. This produces a smoother that responds faster than DEMA without going fully raw. The dual EMA cascade provides additional noise rejection while the zero-lag preprocessing maintains responsiveness.
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## Historical Context
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ZLDEMA extends the zero-lag concept from ZLEMA to double exponential moving averages. Where ZLEMA applies lag compensation to a single EMA, ZLDEMA applies it to a two-stage EMA cascade using the DEMA formula (2*EMA1 - EMA2). This combination targets the middle ground between ZLEMA's speed and TEMA's smoothness.
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## Architecture & Physics
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### Pipeline
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1. **Lag estimate**
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$$\text{lag} = \max(1, \text{round}((N-1)/2))$$
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2. **Zero-lag signal**
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$$s_t = 2 \cdot x_t - x_{t-\text{lag}}$$
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3. **First EMA stage**
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$$\text{EMA1}_t = \text{EMA}(s_t, \alpha)$$
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4. **Second EMA stage**
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$$\text{EMA2}_t = \text{EMA}(\text{EMA1}_t, \alpha)$$
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5. **DEMA output**
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$$\text{ZLDEMA}_t = 2 \cdot \text{EMA1}_t - \text{EMA2}_t$$
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### Warmup compensation
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ZLDEMA uses EMA bias compensation during warmup on both EMA stages:
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$$y_t^{*} = \frac{y_t}{1 - (1 - \alpha)^t}$$
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This avoids the early-stage bias toward zero and makes the first values usable.
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## Math Foundation
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**EMA update:**
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$$y_t = y_{t-1} + \alpha (s_t - y_{t-1})$$
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**Zero-lag signal:**
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$$s_t = 2 \cdot x_t - x_{t-\text{lag}}$$
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**DEMA formula:**
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$$\text{DEMA}_t = 2 \cdot \text{EMA1}_t - \text{EMA2}_t$$
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**Alpha from period:**
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$$\alpha = \frac{2}{N + 1}$$
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## Performance Profile
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### Operation Count (Streaming Mode, Scalar)
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**Hot path (after warmup, compensation complete):**
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| FMA | 4 | 4 | 16 |
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| MUL | 2 | 3 | 6 |
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| **Total** | **6** | | **~22 cycles** |
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The hot path consists of:
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1. Zero-lag signal: `FMA(2.0, val, -lagged)` - 1 FMA
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2. EMA1 core: `FMA(ema1Raw, beta, alpha * signal)` - 1 FMA + 1 MUL
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3. EMA2 core: `FMA(ema2Raw, beta, alpha * ema1)` - 1 FMA + 1 MUL
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4. DEMA output: `FMA(2.0, ema1, -ema2)` - 1 FMA
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**Warmup path (with bias compensation):**
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| FMA | 4 | 4 | 16 |
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| MUL | 4 | 3 | 12 |
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| DIV | 1 | 15 | 15 |
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| CMP | 2 | 1 | 2 |
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| **Total** | **11** | | **~45 cycles** |
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Additional warmup operations:
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- Decay tracking: `e *= beta` - 1 MUL
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- Compensator calc: `1 / (1 - e)` - 1 DIV
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- Bias compensation: `ema1Raw * compensator`, `ema2Raw * compensator` - 2 MUL
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- Hot/compensated checks - 2 CMP
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### Batch Mode (SIMD Analysis)
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ZLDEMA is an IIR filter with lag buffer dependency - not directly vectorizable across bars. However, within-bar operations use FMA intrinsics.
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| Optimization | Benefit |
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| :--- | :--- |
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| FMA instructions | ~22 cycles vs ~28 scalar |
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| stackalloc buffer | Zero heap allocation for lag ≤256 |
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 8/10 | Matches PineScript reference |
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| **Timeliness** | 9/10 | Faster response than DEMA, comparable to ZLEMA |
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| **Overshoot** | 5/10 | Predictive signal plus DEMA amplification causes overshoot |
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| **Smoothness** | 7/10 | Smoother than ZLEMA due to dual EMA cascade |
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## Validation
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ZLDEMA is validated against a PineScript reference implementation.
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| Library | Status | Tolerance | Notes |
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|:---|:---|:---|:---|
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| **TA-Lib** | N/A | - | No ZLDEMA in TA-Lib |
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| **Skender** | N/A | - | No ZLDEMA in Skender |
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| **Tulip** | N/A | - | No ZLDEMA in Tulip |
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| **Ooples** | N/A | - | No ZLDEMA in Ooples |
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| **PineScript** | ✓ Passed | 1e-10 | Matches `lib/trends_IIR/zldema/zldema.pine` |
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## Common Pitfalls
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1. **Increased overshoot on turns**
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The zero-lag signal is a forward estimate, and the DEMA formula (2*EMA1 - EMA2) further amplifies deviations. Expect more overshoot than ZLEMA when price reverses sharply.
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2. **Period semantics**
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ZLDEMA uses EMA alpha; the lag term is derived from period but not equivalent to a window length. Do not compare ZLDEMA period directly to SMA window length.
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3. **Warmup discipline**
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Use `IsHot` / `WarmupPeriod` before acting on signals. Early values are bias-corrected but still unstable. The dual EMA cascade requires longer warmup than single-stage ZLEMA.
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4. **Non-finite data**
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NaN or Infinity is replaced with the last valid value. Before the first valid sample, output is `NaN`.
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5. **DEMA vs ZLDEMA**
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ZLDEMA is not simply DEMA with a different alpha. The zero-lag preprocessing fundamentally changes the input signal, making ZLDEMA more responsive but also more prone to overshoot than standard DEMA. |