mql5/Indicators/MyIndicators/CutlerRSI_MA.md

Cutler's RSI

1. Summary (Introduction)

Cutler's RSI is a variation of the classic Relative Strength Index (RSI) developed by J. Welles Wilder. While the standard RSI uses Wilder's own smoothing method (a type of Smoothed/Running Moving Average), Cutler's version simplifies the formula by using a Simple Moving Average (SMA) to average the positive and negative price changes.

This modification results in an oscillator that can react slightly differently to price movements compared to the standard RSI. It is still a momentum oscillator used to identify overbought and oversold conditions, but its SMA-based calculation gives it a unique character.

The Cutler's RSI Oscillator is a supplementary indicator that displays the difference between the main RSI line and its signal line as a histogram, providing a clearer visual of accelerating and decelerating momentum.

2. Mathematical Foundations and Calculation Logic

The core difference between Cutler's RSI and the standard RSI lies in the smoothing method applied to the price changes.

Required Components

• RSI Period (N): The lookback period for the calculation.
• Source Price (P): The price series used for the calculation (e.g., Close).

Calculation Steps (Algorithm)

1. Calculate Price Changes: For each period, determine the change in price from the previous period. \text{Change}_i = P_i - P_{i-1}

2. Separate Positive and Negative Changes:

   • If \text{Change}_i > 0, then \text{Positive Change}_i = \text{Change}_i and \text{Negative Change}_i = 0.
   • If \text{Change}_i < 0, then \text{Positive Change}_i = 0 and \text{Negative Change}_i = \text{Abs}(\text{Change}_i).

3. Calculate the Simple Moving Average of Changes: This is the defining step. Apply an SMA with period N to both the positive and negative change series. \text{Avg Positive}_i = \text{SMA}(\text{Positive Change}, N)_i \text{Avg Negative}_i = \text{SMA}(\text{Negative Change}, N)_i

4. Calculate the Relative Strength (RS) and Final RSI: \text{RS}_i = \frac{\text{Avg Positive}_i}{\text{Avg Negative}_i} \text{Cutler's RSI}_i = 100 - \frac{100}{1 + \text{RS}_i}

5. Calculate the Signal Line & Oscillator: The signal line is a moving average of the Cutler's RSI line, and the oscillator is the difference between the two.

3. MQL5 Implementation Details

Our MQL5 implementations were refactored for maximum stability, clarity, and computational efficiency.

• Stability via Full Recalculation: We employ a "brute-force" full recalculation within the OnCalculate function for maximum stability.

• Efficient RSI Calculation: Instead of using multiple loops or inefficient SimpleMA calls on every bar, we calculate the Cutler's RSI in a single for loop using an efficient sliding window sum technique. This is mathematically equivalent to an SMA but significantly faster.

• Self-Contained Logic: The indicators are completely self-contained. They do not use external handles and directly process the price arrays provided by OnCalculate.

• Fully Manual MA Calculations: To guarantee 100% accuracy and consistency, all moving average calculations for the signal line (SMA, EMA, SMMA, LWMA) are performed manually. This makes the indicators independent of the <MovingAverages.mqh> library and ensures robust behavior on non-timeseries arrays.

• Indicator Family:

  • Line Versions: CutlerRSI_MA.mq5 plots the RSI line and its signal line.
  • Oscillator Versions: CutlerRSI_Oscillator.mq5 plots the difference between the two lines as a histogram.
  • Heikin Ashi Variants: Both indicators have "pure" Heikin Ashi counterparts, which use the smoothed Heikin Ashi ha_close values as their input.

4. Parameters

• RSI Period (InpPeriodRSI): The lookback period for the SMA of price changes. Default is 14.
• Applied Price (InpAppliedPrice): The source price for the calculation. Default is PRICE_CLOSE.
• Signal Line Settings:
  • InpPeriodMA: The lookback period for the optional signal line.
  • InpMethodMA: The type of moving average for the signal line.

5. Usage and Interpretation

The interpretation of Cutler's RSI is identical to the standard RSI.

• Overbought/Oversold Levels: The primary use is to identify overbought (typically above 70) and oversold (typically below 30) conditions.
• Crossovers:
  • Signal Line Crossover: When the Cutler's RSI line crosses above its moving average, it can be seen as a bullish signal. A cross below is a bearish signal.
  • Centerline Crossover: A crossover of the RSI line above the 50 level indicates that momentum is shifting to bullish. A crossover below 50 indicates bearish momentum.
• Divergence: Look for divergences between the RSI and the price action.
• Oscillator (Histogram): The histogram provides a clear visual of the relationship between the Cutler's RSI and its signal line, highlighting the acceleration and deceleration of momentum.