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Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com> Co-authored-by: aider (openrouter/anthropic/claude-sonnet-4) <aider@aider.chat> Co-authored-by: Warp <agent@warp.dev>
98 lines
3.3 KiB
Markdown
98 lines
3.3 KiB
Markdown
# Moving Average Envelope
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Moving Average Envelope consists of three lines: a moving average in the middle and two lines plotted at a fixed percentage above and below it. The envelope provides a simple way to identify potential support and resistance levels based on a percentage deviation from the average price.
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## Calculation
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```
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Middle = MA(Source, Length)
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Upper = Middle + (Middle × Percentage/100)
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Lower = Middle - (Middle × Percentage/100)
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```
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Where:
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* MA = Moving Average (can be SMA, EMA, or WMA)
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* Source = Price series (typically close price)
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* Length = Lookback period for moving average
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* Percentage = Fixed percentage for band width
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## Parameters
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* Source (default: close) - Price series used for the moving average
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* Length (default: 20) - Period used for moving average calculation
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* Percentage (default: 1.0) - Fixed percentage distance from MA to bands
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* MA Type (default: 1) - Moving average type: 0:SMA, 1:EMA, or 2:WMA
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## Interpretation
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* The middle line shows the average price trend
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* Upper and lower bands create a channel based on fixed percentage
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* Price reaching the bands may indicate overbought/oversold conditions
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* Unlike volatility-based bands, envelope width changes proportionally with price
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* Band penetration may signal potential trend reversals
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* Works best in trending markets with consistent volatility
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## Implementation
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The implementation includes:
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* Choice of three moving average types (SMA, EMA, WMA)
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* Optimized calculations for each MA type
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* Circular buffer for efficient SMA calculation
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* Alpha smoothing for EMA
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* Linear weighting for WMA
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* Proper handling of NA values
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* Input validation
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* Percentage-based band width calculation
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## Performance Profile
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### Operation Count (Streaming Mode, per Bar)
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| Operation | EMA Type | SMA Type | WMA Type | Cost |
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| :--- | :---: | :---: | :---: | :---: |
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| ADD/SUB | 2 | 2 | 1 | 1 cycle |
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| MUL | 4 | 2 | 2 | 3 cycles |
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| DIV | 0 | 1 | 1 | 15 cycles |
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**Per-bar totals:**
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- **EMA type**: 2×1 + 4×3 = ~14 cycles
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- **SMA type**: 2×1 + 2×3 + 1×15 = ~23 cycles (running sum)
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- **WMA type**: 1×1 + 2×3 + 1×15 = ~22 cycles (running sums)
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### Complexity Analysis
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| Mode | Complexity | Notes |
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| :--- | :---: | :--- |
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| Streaming (EMA) | O(1) | IIR recursion, constant time |
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| Streaming (SMA) | O(1) | Running sum with circular buffer |
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| Streaming (WMA) | O(1) | Incremental weight adjustment |
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| Batch | O(n) | Linear scan, n = series length |
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**Memory**: Fixed ~64 bytes state regardless of period.
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### SIMD Analysis
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| Optimization | Applicable | Notes |
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| :--- | :---: | :--- |
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| AVX2 vectorization | ❌ | EMA/SMA recursion prevents parallelization |
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| FMA | ✅ | Band calculation: `Middle ± Middle × factor` |
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| Batch parallelism | Partial | Band calc vectorizable after MA computed |
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 10/10 | Exact computation |
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| **Timeliness** | 5/10 | MA lag inherited (period/2 for SMA) |
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| **Overshoot** | 2/10 | Fixed percentage, no volatility adaptation |
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| **Smoothness** | 7/10 | Follows MA smoothness |
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## Validation
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| **TA-Lib** | N/A | Not implemented |
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| **Skender** | N/A | Not implemented |
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| **Tulip** | N/A | Not implemented |
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| **Ooples** | N/A | Not implemented |
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| **Internal** | ✅ | Mode consistency verified | |