Cyber Cycle Professional

1. Summary (Introduction)

The Cyber Cycle, developed by John Ehlers, is a unique indicator designed to isolate and display the short-term cyclical components of price action. Unlike momentum oscillators like the RSI, which measure the strength of price moves, the Cyber Cycle acts as a band-pass filter to remove trend and high-frequency noise, revealing the underlying "heartbeat" or rhythm of the market.

The output is a smooth, sine-wave-like oscillator whose amplitude (height of the swings) varies with the strength of the cycles. Its primary purpose is not to measure overbought/oversold levels, but to time the turning points of these short-term cycles.

The indicator plots two lines:

Cycle Line: The main filtered value.
Signal Line: The Cycle line delayed by two bars, used for generating crossover signals.

2. Mathematical Foundations and Calculation Logic

The indicator uses a two-pole Butterworth band-pass filter to isolate the cyclical component of the price.

Required Components

Alpha (α): A smoothing factor that determines the center frequency of the band-pass filter (i.e., the length of the cycles it is most sensitive to).
Source Price (P): The price series used for the calculation (Ehlers' original work uses the Median Price (H+L)/2).

Calculation Steps (Algorithm)

Pre-Smoothing: The source price is first lightly smoothed using a 4-bar weighted FIR filter (P + 2*P[1] + 2*P[2] + P[3]) / 6. This reduces some of the extreme noise before the main filter is applied.
Cycle Calculation: The core of the indicator is a recursive Butterworth filter applied to the smoothed price. The formula calculates the current Cycle value based on the change in the smoothed price and the two previous Cycle values: \text{Cycle}_i = (1 - 0.5\alpha)^2 \times (\text{Smooth}_i - 2\text{Smooth}_{i-1} + \text{Smooth}_{i-2}) + 2(1-\alpha)\text{Cycle}_{i-1} - (1-\alpha)^2\text{Cycle}_{i-2}
Signal Line Generation: The Signal Line is simply the Cycle line's value from two bars prior: \text{Signal}_i = \text{Cycle}_{i-2}

3. MQL5 Implementation Details

Self-Contained Calculator (Cyber_Cycle_Calculator.mqh): The entire multi-stage, recursive calculation is encapsulated within a dedicated, reusable calculator class.
Heikin Ashi Integration: An inherited _HA class allows the calculation to be performed seamlessly on smoothed Heikin Ashi data.
Stability via Full Recalculation: The calculation is highly state-dependent. To ensure absolute stability and prevent desynchronization, the indicator employs a full recalculation on every OnCalculate call. This is the most robust method for this type of recursive filter.
Robust Initialization: The calculator includes a simplified, non-recursive calculation for the first few bars to provide a stable "warm-up" period for the main filter, as described in Ehlers' work.

4. Parameters

Alpha (InpAlpha): The smoothing factor for the Butterworth filter. Ehlers' recommendation and a robust starting point is 0.07.
- A lower value (e.g., 0.05) will tune the filter to longer cycles, resulting in a smoother, slower indicator.
- A higher value (e.g., 0.10) will tune the filter to shorter cycles, resulting in a faster, more volatile indicator.
Source (InpSource): Selects between Standard and Heikin Ashi candles. The Median Price of the selected candle type will be used.

5. Usage and Interpretation

The Cyber Cycle is a timing tool for cycle reversals. Its signals are most powerful when used in conjunction with a separate trend-following indicator.

1. Signal Line Crossover (Primary Strategy)

This is the most direct way to use the indicator for entry signals.

Buy Signal: The blue Cycle line crosses above the red Signal line. This indicates that the cycle has turned up from a bottom. The signal is strongest when the crossover occurs below the zero line.
Sell Signal: The blue Cycle line crosses below the red Signal line. This indicates that the cycle has turned down from a top. The signal is strongest when the crossover occurs above the zero line.

CRITICAL RULE: Always Use with a Trend Filter

The Cyber Cycle is not a trend indicator; by design, it removes the trend component to focus on cycles. Trading its signals against a strong trend is a low-probability strategy.

The Problem: In a strong uptrend, the Cyber Cycle will still generate multiple "Sell" signals during minor pullbacks.
The Solution: Add a long-term moving average (e.g., 100 or 200 EMA) to your main chart to define the overall trend.
- Uptrend Rule: Only take Buy signals (Cycle crosses above Signal) when the price is above the long-term moving average.
- Downtrend Rule: Only take Sell signals (Cycle crosses below Signal) when the price is below the long-term moving average.

By following this rule, the Cyber Cycle becomes an excellent tool for timing trend-following entries at the end of corrective pullbacks.

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