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