---
type: Fractal Concept
title: Hurst Exponent
description: Parameter H in (0,1) characterizing long-range dependence and the roughness/persistence of a time series; relates to fractal dimension via D = 2 - H for 1D signals.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/stochastic/hurst-exponent/
tags:
- stochastic
- dimension-theory
aliases:
- hurst
- hurst-exponent
- h-exponent
sources:
- id: glossary
  resource: https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/
  title: Fractal Notebooks glossary (Chapter 4)
- id: seed
  resource: https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml
  title: fractal_rag concept seed (seed.yaml)
generated:
  by: process:fractal-rag-okf-export
  at: "2026-10-24T00:00:00Z"
status: stable
---

# Definition

Parameter H in (0,1) characterizing long-range dependence and the roughness/persistence of a time series; relates to fractal dimension via D = 2 - H for 1D signals.

# Aliases

`hurst`, `hurst-exponent`, `h-exponent`

# Related concepts

* [Fractal](../geometry/fractal.md)
* [Fractal Dimension](../dimension-theory/fractal-dimension.md)

# Citations

[1] [Fractal Notebooks glossary (Chapter 4)](https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/) — `docs/foundations/glossary.md`

[2] [fractal_rag concept seed (seed.yaml)](https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml) — `fractal_rag/src/fractal_rag/concepts/seed.yaml`