Article-22598-Market-Microstructure-GPH-ARFIMA-Estimator

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

Reference/reconstruction repository for the MQL5 article describing the addition of a Geweke-Porter-Hudak (GPH) estimator and ARFIMA-oriented analysis to an existing market microstructure foundation header. The article extends a prior Hurst-analysis framework by estimating the fractional differencing parameter d from log-periodogram regression and validating it against previously computed Hurst values.

The implementation is described as modifications to an existing include file rather than a standalone new project.

Original Article

• Article ID: 22598
• Author: Max Brown
• Publication date: 2026.05.27
• Category: Indicators
• URL: https://www.mql5.com/en/articles/22598

Repository Purpose

This repository serves as a technical reference for reconstructing the article's described additions to MicroStructure_Foundation.mqh:

• GPHEstimator()
• PopulateARFIMAAnalysis()

It documents how the article integrates ARFIMA-style fractional differencing diagnostics into a shared RobustFractalAnalysis workflow, specifically by populating:

• arfima_d
• arfima_confidence

No claim is made that the full original repository or all article files are available here.

Key Concepts

• Geweke-Porter-Hudak log-periodogram regression
• Fractional differencing parameter d
• Relationship between Hurst exponent and differencing:
• d = H - 0.5
• H = d + 0.5
• ARFIMA interpretation:
• d > 0: persistence / positive long memory
• d = 0: random-walk-like behavior
• d < 0: anti-persistence / mean reversion
• Confidence via regression R²
• Validation of d against previously computed Hurst outputs
• Session-level intraday analysis for US100 M1 data

Algorithm / Architecture Summary

The article describes two additions to an existing header-only foundation.

1. GPHEstimator(const double &returns[], int n, double &confidence)

Purpose:

• Estimate fractional differencing parameter d directly from return series.

Method summary:

• Validate minimum bar count.
• Choose low-frequency bandwidth:
• m = floor(N^g)
• default exponent g = 0.65
• Compute the first m periodogram ordinates using a direct DFT.
• Regress:
• log I(ω_j) on log |2 sin(ω_j / 2)|²
• OLS slope gives -d, so:
• d = -slope
• Return regression R² as confidence.
• Clamp d to approximately (-0.49, 0.49).

2. PopulateARFIMAAnalysis(const string symbol, const int tf, const int period, RobustFractalAnalysis &result)

Purpose:

• Fetch close prices
• Build filtered log-return array
• Call GPHEstimator()
• Store outputs into the shared result struct
• Perform H–d consistency diagnostics

Described validation flow:

• Validate symbol and minimum period
• Fetch closes via SafeCopyClose()
• Compute log returns
• Filter invalid prices and artifact returns above ±10%
• Require enough valid returns
• Compute d and confidence
• Compare implied H = d + 0.5 against existing Hurst output when available
• Flag inconsistency if discrepancy exceeds threshold
• Mark low-confidence estimates as unreliable

Constants added in the article

The article states that five constants are added to the existing header:

• GPH_MIN_BARS
• GPH_BANDWIDTH_EXP
• GPH_MIN_FREQ
• GPH_CONF_THRESHOLD
• GPH_D_CONSISTENCY

Mentioned or Attached Files

Explicitly attached files

No attached source files were available in the processed input.

Files mentioned in the article text

• MQL5/Indicators/HurstProfile/HurstProfile.mq5
• MQL5/Indicators/HurstProfile/Includes/MicroStructure_Foundation.mqh

Also mentioned as existing dependencies or related functions/structures:

• RobustFractalAnalysis
• PopulateHurstAnalysis()
• ValidateSymbolV2()
• SafeCopyClose()
• SafeLog()

Statistics

• Series context: Part 3 of a market microstructure series
• Study sample: 72 NY sessions
• Instrument / timeframe: US100 M1
• Session window: 09:30–16:00 ET
• Pooled bars: 27,930
• Pooled GPH estimate: d = -0.006
• Implied pooled H: 0.494
• Pooled regression confidence (R²): 0.0001
• Session-level mean d: -0.016
• Session-level median d: -0.012
• Session-level standard deviation: 0.153
• Interquartile range: [-0.124, 0.084]
• Regime breakdown:
• d < -0.1: 21 sessions (29.2%)
• -0.1 <= d <= 0.1: 34 sessions (47.2%)
• d > 0.1: 17 sessions (23.6%)

Tags

mql5, market-microstructure, arfima, gph, hurst-exponent, fractional-differencing, spectral-analysis, time-series

Difficulty

Intermediate to advanced.

Limitations

• The full original source code repository is unavailable from the provided input.
• No attached .mq5 or .mqh files were included in the processed input.
• This README is based on article content and code excerpts only.
• Metadata such as author, publication date, and category were not provided in the input and therefore cannot be verified here.
• The project appears to be an incremental modification of an existing codebase from earlier articles, so it is not self-contained from this article alone.

Reference

Original article: https://www.mql5.com/en/articles/22598