Article-22015-Fixed-Width-Fractional-Differentiation-MQL5/README.md

Article-22015-Fixed-Width-Fractional-Differentiation-MQL5

This repository is an article-derived reference project based on the original MQL5 article. It does not claim to reproduce the full original source code unless files are explicitly attached.

Overview

This project documents an MQL5 implementation of fixed-width fractional differentiation (FFD) for live MetaTrader 5 data feeds. The article presents a reusable CFFDEngine class for weight generation and dot-product computation, a custom indicator wrapper, and a validation workflow against a Python reference pipeline.

The implementation focus is practical deployment: precomputed weights, bounded lookback, no per-tick allocation, and efficient prev_calculated handling for indicator execution.

Original Article

• Article ID: 22015
• Title: Fixed-Width Fractional Differentiation in MQL5
• Author: Patrick Murimi Njoroge
• Publication date: 2026.05.06
• Category: Python / Scripts / Indicators
• URL: https://www.mql5.com/en/articles/22015

Repository Purpose

This repository serves as a reference/reconstruction project for the article's MQL5 FFD engine and surrounding examples.

Its purpose is to preserve the article-described architecture and code structure for:

• production-style FFD computation in MQL5
• indicator-based visualization
• EA-side integration
• numerical validation against a Python implementation

Key Concepts

• Fixed-width fractional differentiation (FFD)
• Threshold-driven weight truncation
• Header-only MQL5 engine design
• Dot-product computation over bounded windows
• prev_calculated optimization in custom indicators
• Safe logarithmic transform with lower clipping
• EA integration via iCustom or direct embedding
• Cross-validation against Python / AFML workflow

Algorithm / Architecture Summary

The article describes an engine-centered design:

1. Initialization

• Validate d and threshold parameters.
• Build the FFD weights using the recurrence w_k = -w_{k-1} * (d - k + 1) / k
• Stop when abs(w_k) falls below the threshold.
• Reverse the weights so the oldest observation aligns with the oldest lag.

2. Single-bar computation

• Use the last width + 1 prices.
• Optionally apply ln(max(price, 1e-8)).
• Compute a direct dot product between the weight vector and the selected window.

3. Indicator mode

• Fill an output buffer for chart display.
• Use prev_calculated to avoid full recomputation on every tick.
• Mark insufficient-history bars as EMPTY_VALUE.

4. EA integration

• Either consume the indicator via iCustom/CopyBuffer
• Or embed the engine directly and fetch the minimal required history via CopyClose

5. Validation

• Export MQL5 results to CSV.
• Recompute equivalent FFD values in Python.
• Compare maximum absolute difference, targeting sub-1e-12 discrepancy.

Mentioned or Attached Files

Explicitly attached files

• FFDEngine.mqh — header-only CFFDEngine implementation for weight generation and FFD computation
• FFD.mq5 — custom indicator wrapper for plotting the FFD series
• FFDValidation.mq5 — MQL5 script for exporting validation data to CSV
• ffd_cross_validate.py — Python script for cross-checking MQL5 output against Python FFD calculations

Files mentioned in the article text

• No additional source files were identified beyond the attached files listed by the article.

Statistics

• Core engine component: 1 header-only class (CFFDEngine)
• Primary deployment modes described: 3
• custom indicator
• direct EA embedding
• multi-feature multi-engine usage
• Typical width examples:
• d = 0.4, τ = 1e-5 → width ≈ 1457 bars
• d = 0.4, τ = 1e-4 → width ≈ 281 bars
• Performance ranges mentioned:
• width range: 200–4000 bars
• compute time per bar: < 1 ms
• memory per engine: < 40 KB
• Validation tolerance target: max absolute difference < 1e-12

Tags

mql5, fractional-differentiation, ffd, quant, timeseries, custom-indicator, expert-advisor, python-validation, metaTrader5

Difficulty

Intermediate to Advanced

Requires familiarity with:

• MQL5 indicators and EAs
• time-series preprocessing
• numerical methods
• MetaTrader buffer and history APIs
• validation of cross-language implementations

Limitations

• The repository is article-derived; full independently verified source packaging is not available unless the attached files are actually present in the processed repository input.
• Publication date and category were not available in the provided article extract.
• The README reflects the article narrative and code excerpts; it does not claim additional implementation details beyond what was explicitly shown.
• No build or installation workflow is documented here beyond the file placement conventions described in the article.
• If the actual repository does not contain the attached files, then this project should be treated as a reconstruction/reference only.

Reference

• Patrick M. Njoroge, MQL5 Article 22015
• Related prior article mentioned: Part 1 on theory and Python implementation of fractional differentiation