Average True Range (ATR) Pro

1. Summary (Introduction)

The Average True Range (ATR) is a technical analysis indicator developed by J. Welles Wilder. The ATR is not used to indicate price direction; rather, it is a measure of volatility.

It calculates the "true range" for each period and then smooths these values, providing a representation of the average size of the price range. High ATR values indicate high volatility, while low ATR values indicate low volatility.

Our ATR_Pro implementation is a unified, professional version that allows the calculation to be based on either standard or Heikin Ashi candles. Furthermore, it can display the ATR value in two modes:

Points: The classic representation, showing the absolute volatility in price points.
Percent: A normalized value, showing the ATR as a percentage of the closing price, which is useful for comparing volatility across different instruments.

2. Mathematical Foundations and Calculation Logic

The ATR is based on the concept of the "True Range" (TR), which provides a more comprehensive measure of a single period's volatility.

Calculation Steps (Algorithm)

Calculate the True Range (TR): For each bar, the True Range is the greatest of the following three values:
- The current High minus the current Low: \text{High}_i - \text{Low}_i
- The absolute value of the current High minus the previous Close: \text{Abs}(\text{High}_i - \text{Close}_{i-1})
- The absolute value of the current Low minus the previous Close: \text{Abs}(\text{Low}_i - \text{Close}_{i-1})
Calculate the Average True Range (ATR): The ATR is a smoothed moving average of the TR values, calculated using Wilder's specific smoothing method (RMA/SMMA).
- Initialization: The first ATR value is a simple average of the first N TR values.
- Recursive Calculation: All subsequent values are calculated using the following formula: \text{ATR}_i = \frac{(\text{ATR}_{i-1} \times (N-1)) + \text{TR}_i}{N}
Normalize to Percentage (Optional): If the user selects the "Percent" display mode, the final ATR value is converted to a percentage of the closing price.
- \text{ATR\%}_i = \frac{\text{ATR}_i}{\text{Close}_i} \times 100

Note: Our smoothing method is the globally accepted standard for ATR. The built-in iATR in MetaTrader uses a different, non-standard algorithm.

3. MQL5 Implementation Details

Modular Calculation Engine (ATR_Calculator.mqh): All core calculation logic is encapsulated within a reusable include file. The engine now includes a final, optional step to convert the result to a percentage based on a user-selected mode.
Optimized Incremental Calculation: Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.
- It utilizes the prev_calculated state to determine the exact starting point for updates.
- Persistent State: The internal buffers (like m_tr and m_atr_raw) persist their state between ticks. This allows the recursive Wilder's Smoothing algorithm to continue seamlessly from the last known value without re-processing the entire history.
- This results in O(1) complexity per tick, ensuring instant updates and zero lag, even on charts with extensive history.
Object-Oriented Design (Inheritance): A base class, CATRCalculator, handles the shared Wilder's smoothing algorithm. A derived class, CATRCalculator_HA, overrides only the initial calculation of the raw True Range values to use Heikin Ashi candles.

4. Parameters (`ATR_Pro.mq5`)

ATR Period (InpAtrPeriod): The lookback and smoothing period for the indicator. Wilder's original recommendation is 14.
Display Mode (InpDisplayMode): Allows the user to select the output format.
- ATR_POINTS: Displays the ATR in absolute price points (default).
- ATR_PERCENT: Displays the ATR as a percentage of the closing price.
Candle Source (InpCandleSource): Allows the user to select the candle type for the True Range calculation (CANDLE_STANDARD or CANDLE_HEIKIN_ASHI).

5. Usage and Interpretation

Volatility Gauge: A rising ATR indicates that volatility is increasing. A falling ATR indicates that volatility is decreasing.
Stop-Loss Placement: ATR is a cornerstone of risk management. A common technique is to place a stop-loss at a multiple of the ATR (e.g., 2 x ATR) from an entry price.
Position Sizing: ATR can be used to normalize position sizes across different instruments.
Cross-Market Volatility Comparison (Percent Mode): The "Percent" mode is exceptionally useful for comparing the relative volatility of different instruments. For example, you can objectively determine if EURUSD (with a 0.5% ATR) is currently more or less volatile than Gold (with a 1.2% ATR), regardless of their different price levels.
Caution: ATR does not provide any information about trend direction.

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