Estimating Fractional Differencing with the GPH Log-Periodogram

Summary

The article introduces the Geweke–Porter–Hudak estimator for measuring the fractional differencing parameter d from the low-frequency slope of a log-periodogram. It distinguishes this estimate from the Hurst exponent: the measures are theoretically linked, but can disagree when short-range autocorrelation, structural breaks, or non-stationarity are present. A bandwidth selects the low-frequency points used in the regression, and the regression’s R-squared serves as a confidence indicator. The MQL5 implementation calculates selected Fourier components directly and checks the estimate against a Hurst result.

An empirical study of US100 one-minute returns across New York sessions finds d near zero, consistent with earlier Hurst estimates near the random-walk boundary. The author interprets this as support for ordinary return differencing in that sample, while treating weak regression fit as a reason for caution. The estimator diagnoses observed memory structure; it does not by itself prove a tradable signal or guarantee that the same result applies to other instruments, timeframes, or market regimes.

Key ideas

• The GPH method estimates fractional differencing from a regression on low-frequency periodogram values.
• The Hurst exponent and fractional differencing parameter are related but measured differently and may diverge in real data.
• Bandwidth determines how many low-frequency points enter the estimate, while regression fit is used as a reliability check.
• The reported US100 intraday sample has an estimate near the random-walk boundary, but the finding is specific to the observed data.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.