Fixed-Width Fractional Differencing (FFD) - indicator for MetaTrader 5

Raw forex and futures prices are non-stationary: standard regression and classification models trained on them face severe look-ahead bias and spurious correlations. The naive fix — integer differencing — eliminates non-stationarity but destroys all price memory in the process, discarding the very autocorrelation structure that a predictive model needs.

Fixed-width fractional differencing (FFD), introduced in Chapter 5 of Advances in Financial Machine Learning (López de Prado, 2018), resolves this by differencing at a non-integer order d ∈ (0, 1) that is just sufficient for stationarity while retaining maximum memory. This submission provides a production-grade MQL5 implementation of that method.

Two-panel illustration of FFD output: non-stationary raw price (a) and stationary FFD series (b) with the lookback window marked

Components

• FFDEngine.mqh — Header-only library containing the CFFDEngine class. Provides Init(), Compute() (single bar), and ComputeBuffer() (full indicator buffer with prev_calculated optimization). No dynamic memory allocation after OnInit().
• FFD.mq5 — Custom indicator that wraps CFFDEngine. Draws the FFD series in a separate chart window. Supports all ENUM_APPLIED_PRICE values.

How the Algorithm Works

The weight vector is defined by the recurrence (AFML eq. 5.4):

w[0] = 1 w[k] = -w[k-1] * (d - k + 1) / k, k = 1, 2, ...

Iteration stops when |w[k]| < threshold. The vector is then reversed so the oldest price in the lookback window receives the smallest weight and the newest price receives 1.0. The FFD value at bar i is the dot product of the reversed weight vector with the log-price window [i−width, …, i].

For d = 0.4 and threshold = 1e-5, the window width is 1 457 bars. For threshold = 1e-3 it is 54 bars. The threshold controls the stationarity–memory tradeoff: smaller values preserve more memory at the cost of a wider lookback requirement.

Input Parameters

Installation

1. Copy FFDEngine.mqh to your MQL5\Include\ folder (or the subfolder specified during CodeBase download — see file locations below).
2. Copy FFD.mq5 to MQL5\Indicators\Downloads\ (placed there automatically on CodeBase download).
3. Compile both files in MetaEditor. The indicator should compile without warnings under #property strict.
4. Attach FFD to any chart. The indicator window will appear below the main chart after the lookback window (width + 1 bars) has been filled.

Using CFFDEngine in Your Own EA or Indicator

FFDEngine.mqh is a header-only library. Include it and call Init() once in OnInit():

#include <FFDEngine.mqh>

//--- Global instance of the Fixed-Width Fractional Differencing engine
CFFDEngine g_engine;

//+------------------------------------------------------------------+
//| Expert initialization function                                   |
//+------------------------------------------------------------------+
int OnInit()
  {
//--- Initialize FFD engine with d=0.4, threshold=1e-5, and Log Transform enabled
//--- This configuration builds a static memory weight window during the EA initialization phase
   if(!g_engine.Init(0.4, 1e-5, true))
     {
      Print("FFD engine init failed");
      return(INIT_FAILED);
     }
   return(INIT_SUCCEEDED);
  }

//+------------------------------------------------------------------+
//| Expert tick function                                             |
//+------------------------------------------------------------------+
void OnTick()
  {
//--- Query the engine to find out exactly how many historical bars are required
//--- to compute a valid FFD value based on the threshold cutoff
   int need = g_engine.GetMinBars();
   double close[];

//--- Fetch the required depth of historical price data.
//--- If history is not yet synchronized or insufficient, skip execution to avoid errors.
   if(CopyClose(_Symbol, _Period, 0, need, close) < need)
      return;

//--- Ensure the array indexing matches chronological order (oldest bar at index 0)
//--- to correctly align with the reversed FFD weight vector matrix transformations
   ArraySetAsSeries(close, false);

//--- Compute the stationary, fractional-differenced output value for the current live bar
   double ffd_value = g_engine.Compute(close, need);

//--- Use ffd_value as a feature for your model.
  }

Cross-Validation Against Python

The companion file FFDValidation.mq5 (available in the article download) exports FFD values to a CSV file. The Python script ffd_cross_validate.py recomputes the same values using the afml library and compares bar-by-bar. On 5 000 bars of EURUSD H1 with d = 0.4 and threshold = 1e-5, the maximum absolute difference is below 1e-12.

Performance Notes

• Weight vector allocation: once in OnInit(). Zero allocation on the tick path.
• Per-bar computation: O(width) dot product. On modern hardware, a dot product over 1 457 elements completes in under 50 μs.
• ComputeBuffer() uses the prev_calculated argument to skip already-computed bars — only the current incomplete bar is recomputed on each tick.

References and Companion Article

• López de Prado, M. (2018). Advances in Financial Machine Learning, Chapter 5 (Fractional Differentiation), pp. 76–95. Wiley.
• Full theory, Python implementation, and ADF-based parameter search: Feature Engineering for ML — Part 2: Implementing Fixed-Width Fractional Differentiation in MQL5 by Patrick M. Njoroge.
• Companion validation tools: FFDValidation.mq5 and ffd_cross_validate.py — included in the article download package.