Interpreting Conflicting Hurst Exponent and Variance Ratio Results

Summary

The document raises a time-series interpretation problem: a Hurst exponent above 0.5 is understood by the questioner as evidence of persistence, while a variance ratio test appears to indicate mean reversion. It asks which result to trust and why the two diagnostics might disagree. The focus is on how to interpret competing statistical measures when assessing financial series behavior.

No data, test settings, or answer are included, so the document does not establish that either result is correct or explain the source of the discrepancy. The apparent conflict cannot be resolved from the stated findings alone; interpretation would depend on details such as the series being tested, the variance-ratio horizon, assumptions, and estimation uncertainty. The note is therefore useful as a framing of a diagnostic question, rather than as evidence for a trading rule or a conclusion about mean reversion.

Key ideas

• The question reports a Hurst exponent above 0.5 alongside a variance ratio result interpreted as mean reverting.
• It asks how to reconcile the two statistical diagnostics and which interpretation is appropriate.
• No data, test specifications, or response are provided, so the reported conflict cannot be independently assessed.
• Conclusions would depend on the tested series, horizons, assumptions, and uncertainty of each estimate.

Tags

# Variance Ratio Test shows mean-reverting trend but Hurst exponent is greater than 0.5


# Variance Ratio Test shows mean-reverting trend but Hurst exponent is greater than 0.5












I believe Hurst Exponent greater than 0.5 indicates persistent series, meaning the values are not mean-reverting. However, when I run a variance ratio test, I get a graph clearly showing mean reverting trend and I don't quite know how to interpret this information. Which one should I believe and why do I get this result?

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