mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-17 18:18:04 +00:00
65 lines
3.1 KiB
Markdown
65 lines
3.1 KiB
Markdown
# MAMA: MESA Adaptive Moving Average
|
|
|
|
> "John Ehlers again. This time, he built a moving average that doesn't just adapt to volatility—it adapts to the phase of the market cycle. It's like having a GPS for your trend."
|
|
|
|
MAMA (MESA Adaptive Moving Average) is a unique adaptive moving average that uses the Hilbert Transform to determine the phase rate of change of the market cycle. It produces two outputs: MAMA (the adaptive average) and FAMA (Following Adaptive Moving Average), which acts as a slower, confirming signal.
|
|
|
|
## Historical Context
|
|
|
|
Introduced by John Ehlers in *MESA and Trading Market Cycles*, MAMA was designed to solve the problem of lag in a fundamentally different way. Instead of using price volatility (like KAMA or VIDYA), it uses the *cycle period*. When the cycle is short (fast market), MAMA speeds up. When the cycle is long (slow market), MAMA slows down.
|
|
|
|
## Architecture & Physics
|
|
|
|
The architecture is a direct application of the Hilbert Transform Homodyne Discriminator.
|
|
|
|
1. **Hilbert Transform**: Decomposes price into In-Phase (I) and Quadrature (Q) components.
|
|
2. **Phase Calculation**: Computes the phase angle from I and Q.
|
|
3. **Alpha Adaptation**: The smoothing alpha is derived from the rate of change of the phase.
|
|
- Fast Phase Change = High Alpha (Fast MA).
|
|
- Slow Phase Change = Low Alpha (Slow MA).
|
|
|
|
### Zero-Allocation Design
|
|
|
|
We maintain the complex state required for the Hilbert Transform without heap allocations.
|
|
|
|
- **RingBuffers**: For the delay lines needed by the Hilbert Transform.
|
|
- **State Struct**: Stores the phasors (I, Q, Re, Im) and previous values.
|
|
- **Fixed Pipeline**: The DSP pipeline is fixed-length, allowing for static optimization.
|
|
|
|
## Mathematical Foundation
|
|
|
|
$$ \text{Phase} = \arctan(Q / I) $$
|
|
|
|
$$ \alpha = \frac{\text{FastLimit}}{\Delta \text{Phase}} $$
|
|
|
|
$$ \text{MAMA}_t = \alpha \cdot P_t + (1 - \alpha) \cdot \text{MAMA}_{t-1} $$
|
|
|
|
$$ \text{FAMA}_t = 0.5 \alpha \cdot \text{MAMA}_t + (1 - 0.5 \alpha) \cdot \text{FAMA}_{t-1} $$
|
|
|
|
## Performance Profile
|
|
|
|
MAMA is computationally intensive due to the trigonometry (`Atan`, `Sin`, `Cos`) involved in the Hilbert Transform.
|
|
|
|
| Metric | Score | Notes |
|
|
| :--- | :--- | :--- |
|
|
| **Throughput** | Low | Trigonometry involved |
|
|
| **Complexity** | O(1) | Constant time update |
|
|
| **Accuracy** | 8/10 | Adapts to market cycle phase |
|
|
| **Timeliness** | 9/10 | Extremely fast response to phase shifts |
|
|
| **Overshoot** | 6/10 | Can overshoot on sudden cycle changes |
|
|
| **Smoothness** | 6/10 | Can be stepped/jagged in transitions |
|
|
|
|
## Validation
|
|
|
|
Validated against Ehlers' original EasyLanguage code.
|
|
|
|
| Provider | Error Tolerance | Notes |
|
|
| :--- | :--- | :--- |
|
|
| **Ehlers** | N/A | Logic matches *MESA and Trading Market Cycles* |
|
|
|
|
### Common Pitfalls
|
|
|
|
1. **Crossover Signals**: The MAMA/FAMA crossover is the primary signal. MAMA crossing over FAMA is bullish.
|
|
2. **Parameters**: `FastLimit` controls the maximum speed (usually 0.5). `SlowLimit` controls the minimum speed (usually 0.05).
|
|
3. **Whipsaws**: While adaptive, MAMA can still get chopped up in markets with no clear cycle (white noise).
|