Article-22598-Market-Microstructure-GPH-ARFIMA-Estimator/README.md

# 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