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.

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)

Calculate Price Changes: For each period, determine the change in price from the previous period. \text{Change}_i = P_i - P_{i-1}
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).
- If \text{Change}_i = 0, then both are 0.
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
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}

3. MQL5 Implementation Details

Our MQL5 implementation was refactored for maximum stability, clarity, and computational efficiency.

Stability via Full Recalculation: We employ a "brute-force" full recalculation within the OnCalculate function. This is our standard practice for all indicators, especially those with a signal line involving recursive calculations (EMA/SMMA), to ensure 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. We maintain a running sum of positive and negative changes, adding the newest value and subtracting the oldest value in each iteration. This is mathematically equivalent to an SMA but significantly faster.
Self-Contained Price Handling: The indicator does not use external handles like iMA. It directly processes the price arrays (open, high, low, close) provided by OnCalculate and includes logic to handle all standard and calculated ENUM_APPLIED_PRICE types.
Robust Signal Line: The optional signal line (a moving average of the Cutler's RSI line) is calculated using our standard, robust switch block.
- For recursive types (EMA, SMMA), the first value is initialized with a manual SMA calculation at the correct starting index to prevent the floating-point overflows that plague less robust implementations.
- For non-recursive types (SMA, LWMA), we safely use the functions from the <MovingAverages.mqh> library.
Heikin Ashi Variant (CutlerRSI_MA_HeikinAshi.mq5):
- Our toolkit also includes a Heikin Ashi version of this indicator. The calculation logic is identical, but it uses the smoothed Heikin Ashi ha_close values as its input.
- This results in a doubly-smoothed oscillator, ideal for traders who want to focus only on the most significant, sustained momentum shifts.

4. Parameters

RSI Period (InpPeriodRSI): The lookback period for the SMA of price changes. Default is 14.
Applied Price (InpAppliedPrice): The source price used for the calculation (e.g., PRICE_CLOSE).
MA Period (InpPeriodMA): The lookback period for the optional signal line.
MA Method (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. A bearish divergence (higher price highs, lower RSI highs) can signal a potential top, while a bullish divergence (lower price lows, higher RSI highs) can signal a potential bottom.
Caution: As a momentum oscillator, it is most effective in ranging or moderately trending markets. In a very strong trend, it can remain in overbought or oversold territory for extended periods.

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