mql5/Indicators/MyIndicators/UltimateOscillator_Pro.md

Ultimate Oscillator (UO) Professional

1. Summary (Introduction)

The Ultimate Oscillator (UO), developed by Larry Williams, is a momentum oscillator designed to address the problem of false divergence signals often found in single-timeframe oscillators. It achieves this by incorporating three different timeframes (short, medium, and long) into a single, weighted oscillator value, providing a smoother and more reliable measure of momentum.

Our UltimateOscillator_Pro implementation is a unified, professional version that includes an optional, fully customizable signal line and allows the calculation to be based on either standard or Heikin Ashi price data.

2. Mathematical Foundations and Calculation Logic

The UO's calculation combines "Buying Pressure" relative to "True Range" over three distinct periods, using Larry Williams' specific definitions for these terms.

Required Components

• Three Periods (N₁, N₂, N₃): The three lookback periods, typically 7, 14, and 28.
• Price Data: The High, Low, and Close of each bar.

Calculation Steps (Algorithm)

1. Calculate Buying Pressure (BP): For each bar, this measures the closing price's position relative to the "true low".

   • \text{True Low}_i = \text{Min}(\text{Low}_i, \text{Close}_{i-1})
   • \text{BP}_i = \text{Close}_i - \text{True Low}_i

2. Calculate True Range (TR): For each bar, this measures the total "true" price excursion.

   • \text{True High}_i = \text{Max}(\text{High}_i, \text{Close}_{i-1})
   • \text{TR}_i = \text{True High}_i - \text{True Low}_i

3. Sum BP and TR over Three Periods: Calculate the moving sums of BP and TR for each of the three periods (N₁, N₂, N₃).

   • \text{SumBP}_1 = \sum_{i=0}^{N_1-1} \text{BP}_{t-i} , \text{SumTR}_1 = \sum_{i=0}^{N_1-1} \text{TR}_{t-i}
   • (Repeat for N₂ and N₃)

4. Calculate Three Averages: For each period, calculate the ratio of the sums.

   • \text{Avg}_1 = \frac{\text{SumBP}_1}{\text{SumTR}_1} , \text{Avg}_2 = \frac{\text{SumBP}_2}{\text{SumTR}_2} , \text{Avg}_3 = \frac{\text{SumBP}_3}{\text{SumTR}_3}

5. Calculate the Final UO: Combine the three averages using a weighted formula (weights of 4, 2, and 1) and scale the result to 100.

   • \text{UO}_t = 100 \times \frac{(4 \times \text{Avg}_1) + (2 \times \text{Avg}_2) + (1 \times \text{Avg}_3)}{4 + 2 + 1}

3. MQL5 Implementation Details

Our MQL5 implementation follows a highly modular, component-based design to ensure accuracy, reusability, and maintainability.

• Modular Calculation Engine (UltimateOscillator_Calculator.mqh): The entire calculation logic is encapsulated within a reusable include file.

  • Composition: The calculator internally uses our universal MovingAverage_Engine.mqh to handle the smoothing of the Signal Line. This allows for advanced smoothing types (like DEMA or TEMA) beyond the standard SMA.

• Optimized Incremental Calculation (O(1)): Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.

  • State Tracking: It utilizes prev_calculated to process only new bars.
  • Persistent Buffers: Internal buffers persist their state between ticks.
  • Sliding Window: The summation of Buying Pressure and True Range is handled by an efficient sliding window logic (sum += new_value; sum -= old_value;), which is significantly faster than recalculating the sum on every bar.

• Object-Oriented Design:

  • A CUltimateOscillatorCalculator base class handles the core UO algorithm.
  • A derived class, CUltimateOscillatorCalculator_HA, inherits from the base class and overrides the data preparation step to use Heikin Ashi prices.

4. Parameters

• Period 1, 2, 3 (InpPeriod1, InpPeriod2, InpPeriod3): The three lookback periods for the oscillator. Defaults are 7, 14, 28.
• Candle Source (InpCandleSource): Allows the user to select the candle type for the calculation (Standard or Heikin Ashi).
• Signal Line Settings:
  • InpDisplayMode: Toggles the visibility of the signal line.
  • InpSignalPeriod: The lookback period for the signal line.
  • InpSignalMAType: The type of moving average for the signal line. Supports: SMA, EMA, SMMA, LWMA, TMA, DEMA, TEMA.

5. Usage and Interpretation

The Ultimate Oscillator is primarily used to identify divergences, which are its most reliable signals, according to Larry Williams.

Bullish Divergence (Primary Buy Signal)

A three-step pattern is required for a buy signal:

1. A bullish divergence occurs: the price makes a lower low, but the UO makes a higher low.
2. The low of the UO during the divergence must be below 30.
3. A buy signal is triggered only when the UO subsequently breaks above the high it made between the two lows of the divergence.

Bearish Divergence (Primary Sell Signal)

A three-step pattern is required for a sell signal:

1. A bearish divergence occurs: the price makes a higher high, but the UO makes a lower high.
2. The high of the UO during the divergence must be above 70 (some sources suggest 50).
3. A sell signal is triggered only when the UO subsequently breaks below the low it made between the two highs of the divergence.

Secondary Signals

• Signal Line Crossovers: If the signal line is enabled, its crossovers with the UO line can provide earlier, shorter-term momentum signals, similar to a MACD or Stochastic.
• Overbought/Oversold: While not its primary purpose, values above 70 can be considered overbought and values below 30 can be considered oversold, especially in ranging markets.