Miha Kralj
33d20f2a18
Complete thin Dx-composition wrapper indicators with full test coverage: - PlusDi/MinusDi: Directional Indicator wrappers (DiPlus/DiMinus from Dx) - PlusDm/MinusDm: Directional Movement wrappers (DmPlus/DmMinus from Dx) - Individual validation tests per indicator directory (TALib, Skender, bounds) - Combined unit tests (DiDm.Tests.cs) and validation tests (DiDm.Validation.Tests.cs) - Quantower wrappers + tests for all 4 indicators - PineScript v6 implementations with compensated RMA - Normalized .md documentation for all indicators and categories - 182 tests passing, 0 failures
6.0 KiB
MAENV: Moving Average Envelope
A fixed percentage above and below a moving average — the simplest envelope assumes symmetry in price behavior.
| Property | Value |
|---|---|
| Category | Channel |
| Inputs | Source (close) |
| Parameters | period (default 20), percentage (default 1.0), maType (default MaenvType.EMA) |
| Outputs | Multiple series (Upper, Lower) |
| Output range | Tracks input |
| Warmup | period bars |
| PineScript | maenv.pine |
- Moving Average Envelope (MA Envelope) constructs symmetric bands at a fixed percentage distance above and below a moving average center line.
- Parameterized by
period(default 20),percentage(default 1.0),matype(default maenvtype.ema). - Output range: Tracks input.
- Requires
periodbars of warmup before first valid output (IsHot = true). - Validated against TA-Lib, Skender, and Tulip reference implementations where available.
Moving Average Envelope (MA Envelope) constructs symmetric bands at a fixed percentage distance above and below a moving average center line. Unlike volatility-adaptive channels (Bollinger, Keltner, ATR Bands) where band width varies with market conditions, MA Envelope uses a constant percentage offset, creating bands whose absolute width scales only with price level. The indicator supports configurable moving average types (SMA, EMA, WMA) for the center line, allowing users to trade off between lag, smoothness, and responsiveness.
Historical Context
Moving Average Envelopes are one of the oldest band-type indicators, predating Bollinger Bands by decades. The concept is straightforward: if a moving average represents "fair value," then price consistently trading a certain percentage above or below that average represents overbought or oversold conditions. The fixed-percentage approach was the standard technique before John Bollinger introduced standard deviation-based adaptive bands in the 1980s.
The simplicity is both the strength and weakness. Percentage envelopes require manual calibration for each instrument and timeframe: a 1% envelope works for low-volatility large-cap equities but is meaningless for cryptocurrency. The percentage must match the asset's typical volatility. Despite this limitation, fixed envelopes remain popular in institutional settings where the known percentage corresponds to a specific risk threshold or margin requirement.
Architecture & Physics
1. Center Line (Configurable MA)
Three moving average types are supported:
SMA (type = 0): O(1) via circular buffer
\text{Middle}_t = \frac{1}{n} \sum_{i=0}^{n-1} x_{t-i}
EMA (type = 1): O(1) via recursive update with warmup compensation
\alpha = \frac{2}{n + 1}
\text{Middle}_t = \frac{\alpha \cdot x_t + (1-\alpha) \cdot \text{raw}_{t-1}}{w_t}
WMA (type = 2): O(n) weighted sum
\text{Middle}_t = \frac{\sum_{i=0}^{n-1} (n-i) \cdot n \cdot x_{t-i}}{\sum_{i=0}^{n-1} (n-i) \cdot n}
2. Fixed Percentage Offset
\text{distance}_t = \text{Middle}_t \times \frac{P}{100}
\text{Upper}_t = \text{Middle}_t + \text{distance}_t
\text{Lower}_t = \text{Middle}_t - \text{distance}_t
3. Scale Invariance
Because the offset is a percentage of the MA value, the bands automatically scale with price level. A 1% envelope on a $100 stock produces $1 bands; on a $10 stock, $0.10 bands. This is multiplicative scaling, not additive.
4. Complexity
O(1) for SMA and EMA modes. O(n) for WMA mode due to the weighted sum.
Mathematical Foundation
Parameters
| Parameter | Description | Default | Constraint |
|---|---|---|---|
period |
Lookback for the moving average (n) |
20 | > 0 |
percentage |
Band distance as percent of MA (P) |
1.0 | > 0 |
ma_type |
Moving average type: 0=SMA, 1=EMA, 2=WMA | 1 (EMA) | \{0, 1, 2\} |
source |
Input price series | close |
Output Interpretation
| Output | Description |
|---|---|
middle |
Moving average center line |
upper |
MA + fixed percentage (overbought threshold) |
lower |
MA - fixed percentage (oversold threshold) |
Performance Profile
Operation Count (Streaming Mode)
MAENV complexity depends on the MA type. Band arithmetic is identical for all three:
SMA mode (type = 0):
| Operation | Count | Cost (cycles) | Subtotal |
|---|---|---|---|
| SUB (oldest from running sum) | 1 | 1 | 1 |
| ADD (new to running sum) | 1 | 1 | 1 |
| DIV (sum / count for SMA) | 1 | 15 | 15 |
| MUL (middle × pct/100) | 1 | 3 | 3 |
| ADD/SUB (middle ± distance) | 2 | 1 | 2 |
| Total (SMA, hot) | 6 | — | ~22 cycles |
EMA mode (type = 1):
| Operation | Count | Cost (cycles) | Subtotal |
|---|---|---|---|
| FMA (EMA update) | 1 | 4 | 4 |
| FMA (weight accumulator) | 1 | 4 | 4 |
| DIV (raw / weight) | 1 | 15 | 15 |
| MUL (middle × pct/100) | 1 | 3 | 3 |
| ADD/SUB (middle ± distance) | 2 | 1 | 2 |
| Total (EMA, hot) | 6 | — | ~28 cycles |
WMA mode (type = 2): O(n) weighted sum per bar, ~4n + 20 cycles.
Batch Mode (SIMD Analysis)
SMA and EMA modes are sequential (running sum or IIR dependency). Band arithmetic is vectorizable:
| Optimization | Benefit |
|---|---|
| Band arithmetic (middle × pct ± dist) | Vectorizable with Vector<double> in batch post-pass |
| SMA running sum / EMA recursion | Sequential |
| WMA weighted sum | Partially vectorizable with Vector.Multiply + reduction |
Resources
- Murphy, J.J. Technical Analysis of the Financial Markets. New York Institute of Finance, 1999. (Moving average envelope fundamentals)
- Bollinger, J. Bollinger on Bollinger Bands. McGraw-Hill, 2001. (Adaptive alternative that replaced fixed envelopes)