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Comparing Generalized Hurst and Wavelet Methods for Hurst Estimation

Article Quant Q&A · Author: steven
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Summary

The document considers how to choose among methods for estimating the Hurst parameter, naming rescaled range, variance rescaled, generalized Hurst exponent, detrended fluctuation and moving average analysis, wavelet spectral density, and Whittle estimation. It does not provide a formal comparison or a procedure for selecting a method for a particular dataset.

One respondent favors the generalized Hurst exponent and wavelet spectral density based on personal experience assessing estimate stability and oscillatory behavior. The response also points to research on Hurst estimation and multifractality as potentially relevant reading. No datasets, quantitative comparisons, or performance results are supplied. The recommendation is therefore an informal judgment rather than an established ranking, and the source itself acknowledges that it is unaware of research comparing the listed approaches. Researchers should treat the preference as a starting point for investigation and assess estimator behavior under their own data characteristics and assumptions.

Key ideas

  • Several distinct methods are available for estimating the Hurst parameter, including generalized Hurst and wavelet spectral approaches.
  • The response informally identifies generalized Hurst and wavelet spectral density as robust in its author's experience.
  • The document gives no controlled comparison or evidence that establishes one method as universally best.
  • Estimator choice should be evaluated in light of stability, oscillatory behavior, and the data being analyzed.

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# which method is the roubust method to estimate the Hurst parameter?


# which method is the roubust method to estimate the Hurst parameter?












I know there exist lots of method to estimate the Hurst parameter, such as R/S, V/S, GHE, DFA, DMA, Wavelet Spectral Density, Whittle and so on. Can you tell me which one is the best one. Is anyone compare these method?

## Answer by KNFZ (score 2)

https://quant.stackexchange.com/a/35735

I would say that - from personal experience, when analyzing the stability of the estimates and their oscillatory behavior - the two most robust techniques are the generalized Hurst exponent, and the Wavelet Spectral Density. However, to my best knowledge there is no research that compares the various methodologies - but a few months ago I found a paper about Hurst exponent and multifractality, it might be an interesting read for you: Algorithm to estimate the Hurst exponent of high-dimensional fractals

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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