mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-12 23:58:04 +00:00
69 lines
2.8 KiB
Markdown
69 lines
2.8 KiB
Markdown
|
# MACD: Moving Average Convergence Divergence
|
||
|
|
|
||
|
|
> "The trend is your friend, until it bends." — Ed Seykota
|
||
|
|
|
||
|
|
The Moving Average Convergence Divergence (MACD) is a trend-following momentum indicator that shows the relationship between two moving averages of a security's price. Developed by Gerald Appel in the late 1970s, it is one of the most popular and versatile indicators in technical analysis.
|
||
|
|
|
||
|
|
## Historical Context
|
||
|
|
|
||
|
|
Gerald Appel created the MACD to reveal changes in the strength, direction, momentum, and duration of a trend in a stock's price. It combines the lagging features of moving averages with the leading characteristics of momentum oscillators.
|
||
|
|
|
||
|
|
## Architecture & Physics
|
||
|
|
|
||
|
|
MACD is composed of three components:
|
||
|
|
|
||
|
|
1. **MACD Line**: The difference between a fast EMA and a slow EMA.
|
||
|
|
2. **Signal Line**: An EMA of the MACD Line.
|
||
|
|
3. **Histogram**: The difference between the MACD Line and the Signal Line.
|
||
|
|
|
||
|
|
- **Inertia**: Moderate (dependent on EMA periods).
|
||
|
|
- **Momentum**: Tracks the convergence/divergence of trends.
|
||
|
|
- **Range**: Unbounded.
|
||
|
|
|
||
|
|
## Mathematical Foundation
|
||
|
|
|
||
|
|
$$ \text{MACD Line} = \text{EMA}_{\text{fast}}(Close) - \text{EMA}_{\text{slow}}(Close) $$
|
||
|
|
$$ \text{Signal Line} = \text{EMA}_{\text{signal}}(\text{MACD Line}) $$
|
||
|
|
$$ \text{Histogram} = \text{MACD Line} - \text{Signal Line} $$
|
||
|
|
|
||
|
|
Standard parameters are (12, 26, 9):
|
||
|
|
|
||
|
|
- Fast EMA: 12 periods
|
||
|
|
- Slow EMA: 26 periods
|
||
|
|
- Signal EMA: 9 periods
|
||
|
|
|
||
|
|
## Performance Profile
|
||
|
|
|
||
|
|
MACD relies on efficient EMA calculations.
|
||
|
|
|
||
|
|
### Zero-Allocation Design
|
||
|
|
|
||
|
|
The implementation uses three internal `Ema` instances. The `Update` method orchestrates the flow of data between them without creating intermediate objects on the heap.
|
||
|
|
|
||
|
|
| Metric | Score | Notes |
|
||
|
|
| :--- | :--- | :--- |
|
||
|
|
| **Throughput** | 26 ns/bar | High performance due to simple EMA calculations. |
|
||
|
|
| **Allocations** | 0 | Zero heap allocations in hot path. |
|
||
|
|
| **Complexity** | O(1) | Constant time update per bar. |
|
||
|
|
| **Accuracy** | 10/10 | Matches external standards exactly. |
|
||
|
|
| **Timeliness** | 8/10 | Lag is inherent to the moving averages used. |
|
||
|
|
| **Overshoot** | 5/10 | Can overshoot during strong trends. |
|
||
|
|
| **Smoothness** | 9/10 | Very smooth due to double smoothing (EMA of EMA). |
|
||
|
|
|
||
|
|
## Validation
|
||
|
|
|
||
|
|
Validated against multiple external libraries to ensure correctness.
|
||
|
|
|
||
|
|
| Library | Status | Notes |
|
||
|
|
| :--- | :--- | :--- |
|
||
|
|
| **QuanTAlib** | ✅ | Validated. |
|
||
|
|
| **TA-Lib** | ✅ | Matches `TA_MACD` exactly. |
|
||
|
|
| **Skender** | ✅ | Matches `GetMacd` exactly. |
|
||
|
|
| **Tulip** | ✅ | Matches `macd` exactly. |
|
||
|
|
| **Ooples** | ✅ | Matches `CalculateMovingAverageConvergenceDivergence`. |
|
||
|
|
|
||
|
|
### Common Pitfalls
|
||
|
|
|
||
|
|
- **Lag**: As a trend-following indicator based on moving averages, MACD lags price action.
|
||
|
|
- **Whipsaws**: In sideways markets, MACD can generate false signals (whipsaws) as the moving averages cross frequently.
|