Hurst Exponent Estimation in Short ARFIMA Series

Summary

The author is trying to identify ARFIMA models and estimate the fractional differencing parameter through the Hurst exponent. They report inconsistent estimates across several software libraries when testing combinations of autoregressive, moving-average, and fractional-difference terms. In particular, estimates diverge more when the fractional parameter is negative, and some methods return Hurst values above one for stationary models.

The post raises methodological concerns about bias and about estimating long-memory parameters from short series of roughly one hundred observations. It does not include a response, compare estimators, or establish which library performs best. The reported outcomes are the author's simulations and should not be treated as a general benchmark. Its research value lies in identifying interactions between AR and MA components, fractional differencing, estimator behavior, and limited sample size that complicate Hurst-based model identification.

Key ideas

• The author uses the Hurst exponent to infer the fractional differencing parameter in ARFIMA models.
• Estimates vary across libraries for models that combine AR, MA, and fractional-difference terms.
• Some tested methods return Hurst values above one in stationary cases.
• The post asks which estimator is suitable for short series but does not answer or resolve the comparison.

Tags

# Problem with Hurst exponent estimation for ARFIMA models


# Problem with Hurst exponent estimation for ARFIMA models












guys.

I try to realize my ARFIMA model identification script in R. I try to find the best method for unbiased Hurst exponent estimation (fractional difference parameter could be found as Hurst - 0.5) via testing different methods on different models with AR, MA, Dfrac parameters. And each library I use gives me strange results for complicated models like this: AR = c(0.8, -0.1, -0.1), MA = c(-0.6, -0.2) and different Dfrac parameter. None of this libraries give me near the correct estimated value. Most difference I get with Dfrac < 0. Most of methods gives me Hurst value > 1 for stationary (for Dint) models. I have 2 questions: 1) Why do I have strange results for complicated models with most of methods (from different libraries like LrdModelling, WaveLetLongMemory, fractal, etc). 2) What's the best library for Dfrac calculation for short time series (N ~ 100)?

Thank you.

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