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75 lines
4.9 KiB
Markdown
75 lines
4.9 KiB
Markdown
# Cutler's RSI
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## 1. Summary (Introduction)
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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.
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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.
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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.
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## 2. Mathematical Foundations and Calculation Logic
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The core difference between Cutler's RSI and the standard RSI lies in the smoothing method applied to the price changes.
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### Required Components
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- **RSI Period (N):** The lookback period for the calculation.
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- **Source Price (P):** The price series used for the calculation (e.g., Close).
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### Calculation Steps (Algorithm)
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1. **Calculate Price Changes:** For each period, determine the change in price from the previous period.
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$\text{Change}_i = P_i - P_{i-1}$
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2. **Separate Positive and Negative Changes:**
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- If $\text{Change}_i > 0$, then $\text{Positive Change}_i = \text{Change}_i$ and $\text{Negative Change}_i = 0$.
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- If $\text{Change}_i < 0$, then $\text{Positive Change}_i = 0$ and $\text{Negative Change}_i = \text{Abs}(\text{Change}_i)$.
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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.
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$\text{Avg Positive}_i = \text{SMA}(\text{Positive Change}, N)_i$
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$\text{Avg Negative}_i = \text{SMA}(\text{Negative Change}, N)_i$
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4. **Calculate the Relative Strength (RS) and Final RSI:**
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$\text{RS}_i = \frac{\text{Avg Positive}_i}{\text{Avg Negative}_i}$
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$\text{Cutler's RSI}_i = 100 - \frac{100}{1 + \text{RS}_i}$
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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.
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## 3. MQL5 Implementation Details
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Our MQL5 implementations were refactored for maximum stability, clarity, and computational efficiency.
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- **Stability via Full Recalculation:** We employ a "brute-force" full recalculation within the `OnCalculate` function for maximum stability.
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- **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.
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- **Self-Contained Logic:** The indicators are completely self-contained. They do not use external handles and directly process the price arrays provided by `OnCalculate`.
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- **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.
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- **Indicator Family:**
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- **Line Versions:** `CutlerRSI_MA.mq5` plots the RSI line and its signal line.
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- **Oscillator Versions:** `CutlerRSI_Oscillator.mq5` plots the difference between the two lines as a histogram.
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- **Heikin Ashi Variants:** Both indicators have "pure" Heikin Ashi counterparts, which use the smoothed Heikin Ashi `ha_close` values as their input.
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## 4. Parameters
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- **RSI Period (`InpPeriodRSI`):** The lookback period for the SMA of price changes. Default is `14`.
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- **Applied Price (`InpAppliedPrice`):** The source price for the calculation. Default is `PRICE_CLOSE`.
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- **Signal Line Settings:**
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- `InpPeriodMA`: The lookback period for the optional signal line.
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- `InpMethodMA`: The type of moving average for the signal line.
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## 5. Usage and Interpretation
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The interpretation of Cutler's RSI is identical to the standard RSI.
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- **Overbought/Oversold Levels:** The primary use is to identify overbought (typically above 70) and oversold (typically below 30) conditions.
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- **Crossovers:**
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- **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.
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- **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.
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- **Divergence:** Look for divergences between the RSI and the price action.
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- **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.
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