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# Stochastic Momentum Index (SMI) Pro
# William Blau's Stochastic Momentum Index (SMI) Pro Suite (Standard & MTF)
## 1. Summary (Introduction)
The Stochastic Momentum Index (SMI), developed by William Blau, is a smoother version of the standard Stochastic Oscillator. It measures the relationship between the closing price and the *midpoint* of its high-low range, rather than the closing price's position within the range.
The **William Blau's Stochastic Momentum Index (SMI) Pro Suite** is an institutional-grade, low-latency cyclical momentum and trend-reversal tracking system. It consists of two highly synchronized indicators: `SMI_Pro` (Standard) and its Multi-Timeframe (MTF) counterpart.
The result is an oscillator that fluctuates around a zero line, providing clearer signals and minimizing erratic behavior.
Standard Stochastic oscillators calculate price location relative to the absolute low of the high-low range, which makes them highly sensitive to micro-noise and causes them to peg prematurely at extremes during strong trends.
Our `SMI_Pro` implementation is a unified, professional version that allows the calculation to be based on either **standard** or **Heikin Ashi** price data, selectable from a single input parameter.
Developed by William Blau, the **Stochastic Momentum Index (SMI)** resolves this limitation by measuring the relative position of the close price relative to the **median (center) of the high-low range** instead:
## 2. Mathematical Foundations and Calculation Logic
$$\text{Median}_t = \frac{\text{HighestHigh}_t + \text{LowestLow}_t}{2}$$
The SMI involves multiple layers of smoothing, using Exponential Moving Averages (EMAs).
$$\text{RelativePrice}_t = C_t - \text{Median}_t$$
### Required Components
By double-smoothing both this relative price and the total high-low range over a double smoothing period ($D$), the SMI generates exceptionally smooth, fourier-stable, and organic momentum waves.
* **%K Period:** The lookback period for finding the highest high and lowest low.
* **%D Period:** The period for the double EMA smoothing.
* **Signal Period:** The period for the final EMA smoothing that creates the signal line.
To deliver maximum quantitative flexibility, this suite elevates Blau's original concept by replacing the hardcoded EMAs with a **5-motor moving average composition**. This allows traders to select *any* moving average type (SMA, EMA, SMMA, LWMA, TMA, DEMA, TEMA, VWMA) for both the double-smoothing stages and the final signal line, introducing volume-weighting (VWMA) capabilities to the entire SMI pipeline for the first time.
### Calculation Steps (Algorithm)
---
1. **Find the Price Range:** For each bar, determine the highest high and lowest low over the `%K Period`.
2. **Calculate the Relative Distance:** Determine the distance of the current close from the midpoint of the high-low range.
$\text{Relative Distance}_i = \text{Close}_i - \frac{\text{Highest High}_i + \text{Lowest Low}_i}{2}$
3. **First EMA Smoothing:** Apply an EMA with the `%D Period` to both the `Relative Distance` and the `Range`.
4. **Second EMA Smoothing:** Apply another EMA with the `%D Period` to the results of the first smoothing.
5. **Calculate the SMI Value:** The final SMI is calculated as a percentage.
$\text{SMI}_i = 100 \times \frac{\text{EMA2(Relative)}_i}{\text{EMA2(Range)}_i / 2}$
6. **Calculate the Signal Line:** The signal line is an EMA of the SMI line itself, using the `Signal Period`.
## 2. Mathematical & Quant Foundations
## 3. MQL5 Implementation Details
The indicator calculates a double-smoothed ratio using five independent, state-safe moving average engines:
Our MQL5 implementation follows a modern, object-oriented design to ensure stability, reusability, and maintainability.
### A. Core Price and Range Calculations
* **Modular Calculation Engine (`SMI_Calculator.mqh`):**
The entire calculation logic is encapsulated within a reusable include file.
* **`CSMICalculator`**: The base class that performs the full, multi-stage SMI calculation on a given set of High, Low, and Close prices.
* **`CSMICalculator_HA`**: A child class that inherits all the complex logic and only overrides the initial data preparation step to use smoothed Heikin Ashi prices as its input. This object-oriented approach eliminates code duplication.
Over the lookback period $K$ (`InpLengthK`), the highest high and lowest low are calculated to determine the high-low range and the relative price distance from the median:
* **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.
* The internal buffers (`m_ema_rel`, `m_ema_range`, etc.) persist their state between ticks, allowing the recursive EMA algorithms to continue seamlessly from the last known value.
* This results in **O(1) complexity** per tick, ensuring instant updates and zero lag, even on charts with extensive history.
$$\text{Range}_t = \max_{j=0 \dots K-1} (H_{t-j}) - \min_{j=0 \dots K-1} (L_{t-j})$$
* **Robust EMA Initialization:** Each recursive EMA calculation step is carefully initialized with a simple average to provide a stable starting point for the calculation chain and prevent floating-point overflows.
$$\text{Relative}_t = C_t - \frac{\max_{j=0 \dots K-1} (H_{t-j}) + \min_{j=0 \dots K-1} (L_{t-j})}{2}$$
## 4. Parameters
### B. Double Smoothing Pipeline
* **%K Length (`InpLengthK`):** The lookback period for finding the highest high and lowest low. Default is `10`.
* **%D Length (`InpLengthD`):** The period used for the double EMA smoothing. Default is `3`.
* **EMA Length (`InpLengthEMA`):** The smoothing period for the final signal line. Default is `3`.
* **Candle Source (`InpCandleSource`):** Allows the user to select the candle type for the calculation (`Standard` or `Heikin Ashi`).
Both the relative price ($\text{Relative}_t$) and the absolute range ($\text{Range}_t$) are processed through two consecutive, state-safe smoothing engines using the slowing period $D$ (`InpLengthD`) and the selected slowing MA type (`InpSlowingType`):
## 5. Usage and Interpretation
$$\text{Sm1\_Rel}_t = \text{Smoothing1}_{D}(\text{Relative}_t)$$
* **Overbought/Oversold Levels:** The SMI typically uses +40 as the overbought level and -40 as the oversold level.
* **Crossovers:**
* **SMI / Signal Line Crossover:** When the SMI line crosses above its signal line, it can be considered a bullish signal. When it crosses below, it's a bearish signal.
* **Zero Line Crossover:** A crossover of the SMI line above the zero line indicates that bullish momentum is taking control. A crossover below zero indicates bearish momentum.
* **Divergence:** Look for divergences between the SMI and the price. A bearish divergence (higher price highs, lower SMI highs) can signal a potential top, while a bullish divergence (lower price lows, higher SMI lows) can signal a potential bottom.
* **Caution:** While smoother than a standard Stochastic, the SMI is still a momentum oscillator and can give false signals in choppy markets.
$$\text{Sm2\_Rel}_t = \text{Smoothing2}_{D}(\text{Sm1\_Rel}_t)$$
$$\text{Sm1\_Ran}_t = \text{Smoothing1}_{D}(\text{Range}_t)$$
$$\text{Sm2\_Ran}_t = \text{Smoothing2}_{D}(\text{Sm1\_Ran}_t)$$
### C. Final SMI & Signal Line Equations
The final SMI represents the ratio of the double-smoothed relative price over half of the double-smoothed absolute range, bounded strictly between $-100$ and $100$:
$$\text{SMI}_t = \begin{cases}
100.0 \times \frac{\text{Sm2\_Rel}_t}{\frac{\text{Sm2\_Ran}_t}{2.0}} & \text{if } \text{Sm2\_Ran}_t > 1.0e-9 \\
0.0 & \text{otherwise}
\end{cases}$$
The final plotted Signal Line is computed by smoothing the active $\text{SMI}_t$ over the signal period (`InpLengthEMA`) using the selected signal MA type (`InpSignalType`):
$$\text{Signal}_t = \text{Smoothing}_{\text{SignalPeriod}}(\text{SMI}_t)$$
---
## 3. Recommended Calibration Presets
| Trading Style | Timeframe | SMI Settings ($K, D, \text{Slowing MA}$) | Signal Settings ($\text{EMA}, \text{Signal MA}$) | Quantitative Tactical Role |
| :--- | :--- | :---: | :---: | :--- |
| **Intraday Scalping** | M5 / M15 | `10, 3` (EMA) | `3` (EMA) | **Fast Mean Reversion.** Highly responsive crossover triggers on intraday charts. |
| **Trend Following** | M30 / H1 | `14, 5` (SMA) | `5` (SMA) | **Stable Swing Tracking.** Filters out noise on H1 charts, tracking clean cyclical waves. |
| **Institutional Flow** | H1 / H4 | `14, 3` (VWMA) | `3` (EMA) | **Volume-Backed Momentum.** Integrates exchange volume weighting to track true institutional pivots. |
---
## 4. Visual & Technical Highlights
* **5-Motor Composite OOP Design:**
To handle double-smoothing across multiple variables cleanly without visual or computational lag, the `CSMICalculator` class instantiates five independent `CMovingAverageCalculator` engines. This modular structure completely isolates the MA calculations, enabling fázis-helyes (phase-correct) and state-safe execution for any combination of MA types.
* **Pragmatic Visual Styling:**
The main oscillator lines are plotted with distinct, professional weights: the SMI line is plotted in bold Steel Blue (`clrSteelBlue`, width 2) for immediate trend identification, while the Signal line is plotted as a thinner Dark Orange line (`clrDarkOrange`, width 1.5) for clean crossover visual comfort.
* **Chronological Safety Guards:**
The engine enforces chronological array indexing (`ArraySetAsSeries(..., false)`) across all internal persistent buffers, price caches, and indicator buffers, completely eliminating phase shift errors during template changes.
---
## 5. Advanced MQL5 MTF Implementation Details
Operating high-order recursive double-smoothings combined with lookback arrays across multiple timeframes requires precise architectural guards:
### A. Non-Warping Staircase Solution
To prevent the active, forming HTF candle from drawing a warped diagonal slope on lower timeframe charts, the indicator runs a backward-scanning block-force loop. It identifies the beginning of the active forming HTF block and rewrites the entire block flat on every tick:
```mql5
int first_bar_of_forming_htf = rates_total - 1;
while(first_bar_of_forming_htf > 0 &&
iBarShift(_Symbol, g_calc_timeframe, time[first_bar_of_forming_htf], false) == 0)
{
first_bar_of_forming_htf--;
}
first_bar_of_forming_htf++; // Anchor start of current HTF period block
if(start > first_bar_of_forming_htf)
start = first_bar_of_forming_htf;
```
### B. High-Order IIR State Mocking
Since the SMI MA double-smoothing relies on deep historical smoothed averages, calling calculations continuously on the live forming bar on every tick can cause feedback decay. To solve this, the MTF engine uses **State Mocking** during live ticks by passing `prev_calculated = g_htf_count`, which updates only the active live register while keeping historical closed states completely locked.
---
## 6. Symmetrical Momentum Trading Strategies
### A. The Symmetrical Extremes Crossover Strategy (40/60 & 80/90 Reversal)
Because the SMI is bounded between $-100$ and $100$, crossovers occurring inside the extreme over-extended zones represent high-probability trend reversal points.
1. **Indicator Setup:**
* **SMI Pro:** K Period = `10`, D Period = `3` (EMA), Signal = `3` (EMA).
2. **Execution Rules:**
* **BUY Trigger:** Enter Long when the **SMI line crosses above the Signal line** strictly while both lines are **below the $-40.0$ or $-60.0$ levels** (Oversold).
* **SELL Trigger:** Enter Short when the **SMI line crosses below the Signal line** strictly while both lines are **above the $+40.0$ or $+60.0$ levels** (Overbought).
3. **Risk Management:** Place Stop Loss below the local swing low (for Long trades) or above the local swing high (for Short trades). Exit on an opposing crossover at the opposite extreme boundary.
### B. The Volume-Weighted Momentum Continuation Squeeze
By utilizing volume-weighted moving averages (VWMA) for the double-smoothing slowing stage, we ensure that trend accelerations are backed by true institutional transaction volume.
1. **Indicator Setup:**
* Load the indicator on an M5 or M15 chart.
* Configure the Slowing MA to **`VWMA`** and the Signal MA to **`EMA`**.
2. **Strategy Mechanics:**
* During consolidation, the SMI and Signal lines contract towards the $0.0$ level, forming a tight squeeze.
* **BUY Entry:** Enter Long when the **SMI line crosses above the Signal line** near the $0.0$ level, accompanied by a breakout of the SMI line above $0.0$. The VWMA double-smoothing ensures this cross is backed by true transaction volume.
* **SELL Entry:** Enter Short when the **SMI line crosses below the Signal line** near the $0.0$ level, and breaks below $0.0$.
3. **Strategic Value:** Entering near the $0.0$ level allows you to catch the very beginning of a trend expansion immediately after a volatility contraction squeeze.