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Toh4iem9
70 lines
5.2 KiB
Markdown
70 lines
5.2 KiB
Markdown
# Kaufman's Adaptive Moving Average (KAMA) Professional
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## 1. Summary (Introduction)
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Kaufman's Adaptive Moving Average (KAMA), developed by Perry J. Kaufman, is a sophisticated "intelligent" moving average designed to be both sensitive to trends and resilient to market noise. It addresses the fundamental trade-off of traditional moving averages: a short period is responsive but prone to whipsaws, while a long period is smooth but suffers from significant lag.
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KAMA solves this by dynamically adjusting its smoothing speed based on the market's directional efficiency. It automatically slows down during choppy, sideways markets and speeds up during clear, trending periods.
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Our `KAMA_Pro` implementation is a definition-true version of this powerful tool, fully supporting calculations on both **standard** and **Heikin Ashi** price data.
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## 2. Mathematical Foundations and Calculation Logic
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The core of KAMA is the **Efficiency Ratio (ER)**, which quantifies the "trendiness" of the market by measuring its signal-to-noise ratio.
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### Required Components
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* **ER Period (N):** The lookback period for calculating the Efficiency Ratio.
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* **Fast EMA Period (F):** The period for the fastest possible EMA (used when the trend is perfect).
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* **Slow EMA Period (S):** The period for the slowest possible EMA (used when the market is pure noise).
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* **Source Price (P):** The price series for the calculation.
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### Calculation Steps (Algorithm)
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1. **Calculate the Efficiency Ratio (ER):** The ER is the ratio of the net directional movement ("Signal") to the total price movement ("Noise") over the period `N`.
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* **Direction (Signal):** The absolute net change in price over `N` periods.
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$\text{Direction}_t = \text{Abs}(P_t - P_{t-N})$
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* **Volatility (Noise):** The sum of the absolute price changes for each bar within the `N` period.
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$\text{Volatility}_t = \sum_{i=0}^{N-1} \text{Abs}(P_{t-i} - P_{t-i-1})$
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* **Efficiency Ratio:**
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$\text{ER}_t = \frac{\text{Direction}_t}{\text{Volatility}_t}$
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*(The value of ER ranges from 0 to 1)*
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2. **Calculate the dynamic Smoothing Constant (SC):** The ER is used to create a dynamic smoothing constant that scales between the fastest and slowest possible speeds.
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* First, define the fastest and slowest smoothing constants based on the EMA formula:
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$\text{sc}_{fast} = \frac{2}{F + 1}$
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$\text{sc}_{slow} = \frac{2}{S + 1}$
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* Then, calculate the scaled smoothing constant and square it to give more weight to the slower end of the range:
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$\text{SC}_t = (\text{ER}_t \times (\text{sc}_{fast} - \text{sc}_{slow}) + \text{sc}_{slow})^2$
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3. **Calculate the KAMA:** The KAMA is calculated recursively, similar to an EMA, but using the dynamic `SC` calculated in the previous step.
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$\text{KAMA}_t = \text{KAMA}_{t-1} + \text{SC}_t \times (P_t - \text{KAMA}_{t-1})$
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## 3. MQL5 Implementation Details
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* **Modular Calculation Engine (`KAMA_Calculator.mqh`):** All mathematical logic is encapsulated in a dedicated include file.
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* **Robust State Management:** KAMA is a recursive filter, meaning its current value depends on its previous value. Our `CKamaCalculator` class implements **correct state management** by storing the previous KAMA value in a member variable (`m_prev_kama`). This is critical for ensuring a stable and accurate calculation that is resilient to chart reloads and timeframe changes.
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* **Object-Oriented Design (Inheritance):** A `CKamaCalculator` base class and a `CKamaCalculator_HA` derived class are used to cleanly separate the logic for standard and Heikin Ashi price sources without code duplication.
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* **Stability via Full Recalculation:** The indicator performs a full recalculation on every tick, which is the most robust approach for a state-dependent, recursive filter like KAMA.
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## 4. Parameters
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* **ER Period (`InpErPeriod`):** The lookback period for the Efficiency Ratio calculation. Kaufman's standard value is `10`.
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* **Fast EMA Period (`InpFastEmaPeriod`):** The period for the fastest EMA speed. Kaufman's standard value is `2`.
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* **Slow EMA Period (`InpSlowEmaPeriod`):** The period for the slowest EMA speed. Kaufman's standard value is `30`.
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* **Applied Price (`InpSourcePrice`):** The source price for the calculation (Standard or Heikin Ashi).
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## 5. Usage and Interpretation
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KAMA is a superior, low-lag trend line that can be used in multiple ways.
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* **Primary Trend Filter:** The main function of KAMA is to identify the direction and state of the trend.
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* When the price is consistently above a rising KAMA, the market is in a strong uptrend.
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* When the price is consistently below a falling KAMA, the market is in a strong downtrend.
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* When the KAMA line **flattens out**, it is a clear and early signal that the market has entered a consolidation or ranging phase, and trend-following strategies should be paused. This is KAMA's key advantage over traditional MAs.
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* **Dynamic Support and Resistance:** In a trending market, the KAMA line acts as a highly responsive dynamic level of support (in an uptrend) or resistance (in a downtrend), providing potential entry points on pullbacks.
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* **Crossover Signals:** Price crossing over the KAMA line can be used as a trade signal, which is often more reliable than traditional MA crossovers due to KAMA's adaptive nature.
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