mql5/Indicators/MyIndicators/DMIStochastic_Pro.md

DMI Stochastic Professional

1. Summary (Introduction)

The DMI Stochastic, developed by Barbara Star, is an innovative oscillator that combines two powerful concepts: J. Welles Wilder's Directional Movement Index (DMI) and the Stochastic Oscillator.

Instead of analyzing the price, this indicator measures the momentum of the underlying directional pressure in the market. It does this by first creating an oscillator from the difference between the Positive (+DI) and Negative (-DI) Directional Indicators, and then feeding this new value series into a standard Stochastic calculation.

The result is an oscillator that identifies overbought and oversold conditions in bullish or bearish momentum itself, providing unique insights into potential trend exhaustion and reversals.

Our DMIStochastic_Pro implementation is a professional version that includes:

• Calculation based on either standard or Heikin Ashi candles.
• A user-selectable formula for the internal DMI Oscillator for more intuitive use.

2. Mathematical Foundations and Calculation Logic

The calculation is a three-stage process: first building the DMI components, then creating the DMI Oscillator, and finally applying the Stochastic formula.

Required Components

• DMI Period (N): The lookback period for the DMI calculation (e.g., 10).
• Stochastic Periods: Fast %K Period, Slowing Period, and %D Period.

Calculation Steps (Algorithm)

1. Calculate Directional Indicators (+DI, -DI): This initial step is identical to the standard ADX calculation.

   • First, the raw Directional Movement (+DM, -DM) and True Range (TR) are calculated for each bar.
   • These three series are then smoothed using Wilder's method (SMMA/RMA) over the DMI Period N.
   • Finally, the +DI and -DI lines are calculated: \text{+DI}_i = 100 \times \frac{\text{Smoothed +DM}_i}{\text{Smoothed TR}_i} \text{-DI}_i = 100 \times \frac{\text{Smoothed -DM}_i}{\text{Smoothed TR}_i}

2. Create the DMI Oscillator: This is the core of the indicator. An oscillator is created from the difference between the two directional indicators. Our implementation allows for two formulas:

   • Intuitive (Default): \text{DMI Oscillator}_i = \text{+DI}_i - \text{-DI}_i (High values indicate strong bullish pressure)
   • Original: \text{DMI Oscillator}_i = \text{-DI}_i - \text{+DI}_i (High values indicate strong bearish pressure)

3. Apply the Slow Stochastic Formula: The DMI Oscillator series is now used as the input for a standard Slow Stochastic calculation.

   • Calculate Fast %K: \text{Highest High} = \text{Highest value of DMI Oscillator over the Fast \%K Period} \text{Lowest Low} = \text{Lowest value of DMI Oscillator over the Fast \%K Period} \text{Fast \%K} = 100 \times \frac{\text{DMI Oscillator}_i - \text{Lowest Low}}{\text{Highest High} - \text{Lowest Low}}
   • Calculate Slow %K (Main Line): The Fast %K series is smoothed using the selected moving average type over the Slowing Period. \text{Slow \%K} = \text{MA}(\text{Fast \%K}, \text{Slowing Period})
   • Calculate %D (Signal Line): The Slow %K series is smoothed again using the selected moving average type over the %D Period. \text{\%D} = \text{MA}(\text{Slow \%K}, \text{\%D Period})

3. MQL5 Implementation Details

Our MQL5 implementation follows the same modern, object-oriented design as our other professional indicators.

• Shared Core Engine (DMI_Engine.mqh): Just like the ADX Pro, this indicator leverages the shared DMI_Engine to perform the initial heavy lifting (calculating +DI and -DI). This guarantees mathematical consistency across the suite.

• Modular Calculation Engine (DMIStochastic_Calculator.mqh): This engine acts as a coordinator. It:

  1. Delegates the DMI calculation to the DMI_Engine.
  2. Calculates the DMI Oscillator from the engine's output.
  3. Delegates the Stochastic smoothing to two instances of the MovingAverage_Engine.

• Engine Integration: The calculator internally uses two instances of our universal MovingAverage_Engine.mqh to handle the smoothing of the Slow %K and the %D Signal Line. This allows for advanced smoothing types (like DEMA or TEMA) beyond the standard SMA.

• Optimized Incremental Calculation (O(1)): The entire chain of engines (DMI Engine -> DMI Stoch Calculator -> MA Engines) is fully optimized for incremental calculation using prev_calculated. State is preserved across all layers.

• Object-Oriented Design:

  • The Heikin Ashi version (CDMIStochasticCalculator_HA) works by injecting the Heikin Ashi version of the DMI Engine (CDMIEngine_HA) into the calculation pipeline.

4. Parameters

• Candle Source (InpCandleSource): Selects the candle type for the initial DMI calculation.
  • CANDLE_STANDARD: Uses standard OHLC data.
  • CANDLE_HEIKIN_ASHI: Uses smoothed Heikin Ashi data.
• Oscillator Formula (InpOscType): Determines the formula for the internal DMI Oscillator.
  • OSC_PDI_MINUS_NDI: High values represent bullish pressure (recommended, intuitive).
  • OSC_NDI_MINUS_PDI: High values represent bearish pressure (original definition).
• DMI Period (InpDMIPeriod): The lookback period for the underlying +DI and -DI calculation. (Default: 10).
• Stochastic %K Period (InpFastKPeriod): The lookback period for finding the highest/lowest values of the DMI Oscillator. (Default: 10).
• Stochastic %K Slowing (InpSlowKPeriod): The period for the first smoothing of the raw %K line. (Default: 3).
• Stochastic %D Period (InpSmoothPeriod): The period for smoothing the main %K line to create the signal line. (Default: 3).
• MA Method for Stochastic (InpStochMethod): The type of moving average to use for the %K slowing step. (Default: SMA).
• MA Method for Signal (InpSignalMethod): The type of moving average to use for the %D smoothing step. (Default: SMA).

5. Usage and Interpretation

The DMI Stochastic should be interpreted as a momentum-of-momentum oscillator. It shows when the bullish or bearish pressure is overextended. (Assuming default PDI - NDI formula).

• Overbought/Oversold Momentum:
  • Values > 80 (Overbought): Indicates that bullish pressure has been extremely strong and dominant. This may signal that the bullish move is exhausted and a bearish reversal or consolidation is imminent.
  • Values < 20 (Oversold): Indicates that bearish pressure has been extremely strong. This may signal that the bearish move is exhausted and a bullish reversal or consolidation is likely.
• Crossovers:
  • When the %K line (blue) crosses above the %D line (red), it signals a bullish shift in directional momentum.
  • When the %K line (blue) crosses below the %D line (red), it signals a bearish shift in directional momentum.