Discussing the article: "Market Microstructure in MQL5: Estimating ARFIMA d with GPH (Part 3)"
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Check out the new article: Market Microstructure in MQL5: Estimating ARFIMA d with GPH (Part 3).
A GPH‑based estimator for d, the key ARFIMA parameter, is added to MicroStructure_Foundation.mqh. GPHEstimator() computes d via log‑periodogram regression, while PopulateARFIMAAnalysis() stores d with an R² confidence score and validates the theoretical relationship H = d + 0.5. An empirical study on 72 US100 M1 sessions confirms pooled d = −0.006, consistent with the random walk boundary established in Part 2.
Part 1 of this series built a defensive foundation: guarded math, validated price feeds, and stable statistical primitives. Part 2 added three Hurst estimators and established a key empirical result for US100 M1 Globex futures: the confidence‑weighted H hovers near 0.5, with the pooled post‑open estimate at 0.511 and the rolling bar‑by‑bar mean at approximately 0.48. All three estimators straddle the random walk boundary.
That result raises a precise engineering question. H tells us whether memory exists and in which direction. It does not tell us how much fractional differencing a price series requires to become stationary. A trading system that applies standard integer differencing—taking first differences, d = 1—to a series with a true differencing parameter of d = 0.3 is over‑differencing it. Genuine long‑range structure is destroyed. A system that applies no differencing to a series with d = 0.4 leaves non‑stationarity in the feature.
The Geweke‑Porter‑Hudak (GPH) estimator solves a different problem from the Hurst exponent. Where Hurst measures the self‑similarity exponent of a time series, GPH directly estimates the fractional differencing parameter d from the slope of the log‑periodogram. The two quantities are theoretically linked by d = H − 0.5, but they are measured by different methods and disagree in the presence of short‑range autocorrelation, non‑stationarity, or structural breaks. Running both provides a consistency check that neither measurement alone can offer.
This article adds two functions to MicroStructure_Foundation.mqh: GPHEstimator() and PopulateARFIMAAnalysis(). They estimate d via log‑periodogram regression, write the result to RobustFractalAnalysis.arfima_d, and validate it against the Hurst output from Part 2. An empirical study on 72 NY sessions of US100 M1 data confirms that d is close to zero—consistent with Part 2—and quantifies the session‑to‑session variation.
Author: Max Brown