[2605.21316] Bitcoin's Power Law: Weak Structure, Strong Forecasts

-->

Statistics > Applications

arXiv:2605.21316 (stat)

[Submitted on 20 May 2026]

Title:Bitcoin's Power Law: Weak Structure, Strong Forecasts

Authors:Carlos Baquero, Raquel Menezes<br>View a PDF of the paper titled Bitcoin's Power Law: Weak Structure, Strong Forecasts, by Carlos Baquero and 1 other authors

View PDF<br>HTML (experimental)

Abstract:Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^{\beta}$ with $\hat\beta \approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant distributional series, and develop three principled time-domain adaptations of the protocol. We find that (i) the distributional power law is rejected on UTXO balances and daily |returns|, with lognormal preferred decisively; (ii) the fitted time-domain exponent varies by nearly a factor of three across reasonable shifts of the time origin -- it is not specification-robust in the sense required for a shift-invariant structural reading; (iii) standard residual diagnostics and scale-invariance tests proposed in earlier work cannot distinguish a power law from a multi-component sigmoid stack fit to the same data; (iv) Bitcoin price stands apart in a cross-asset comparison spanning Bitcoin on-chain metrics and traditional asset classes: it is the only series in the nine-series in-sample test where no single-component growth curve improves on the power law, and the quarterly $K=3$ wave-stability bootstrap rejects the PL+AR(1) null on Bitcoin at $p = 0.015$ (strict 15% CV threshold) -- a clear cross-asset separation, although not a Bonferroni-robust rejection; and (v) walk-forward Diebold-Mariano evaluation against ten candidates -- including standard time-series baselines (RW with drift, auto-ARIMA, ETS, local-linear-trend) -- shows the in-sample winner (multi-sigmoid) is among the worst long-horizon forecasters, while the simple power law dominates 12-24 month horizons against every standard baseline at $p

Subjects:

Applications (stat.AP); Distributed, Parallel, and Cluster Computing (cs.DC)

MSC classes:<br>62M10, 62M20, 62P05, 91B84

ACM classes:<br>G.3

Cite as:<br>arXiv:2605.21316 [stat.AP]

(or<br>arXiv:2605.21316v1 [stat.AP] for this version)

https://doi.org/10.48550/arXiv.2605.21316

Focus to learn more

arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Carlos Baquero [view email]<br>[v1]<br>Wed, 20 May 2026 15:46:46 UTC (258 KB)

Full-text links:<br>Access Paper:

View a PDF of the paper titled Bitcoin's Power Law: Weak Structure, Strong Forecasts, by Carlos Baquero and 1 other authors<br>View PDF<br>HTML (experimental)<br>TeX Source

view license

Current browse context:

stat.AP

next >

new<br>recent<br>| 2026-05

Change to browse by:

cs<br>cs.DC<br>stat

References & Citations

NASA ADS<br>Google Scholar

Semantic Scholar

export BibTeX citation<br>Loading...

BibTeX formatted citation

&times;

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer (What is the Explorer?)

Connected Papers Toggle

Connected Papers (What is Connected Papers?)

Litmaps Toggle

Litmaps (What is Litmaps?)

scite.ai Toggle

scite Smart Citations (What are Smart Citations?)

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv (What is alphaXiv?)

Links to Code Toggle

CatalyzeX Code Finder for Papers (What is CatalyzeX?)

DagsHub Toggle

DagsHub (What is DagsHub?)

GotitPub Toggle

Gotit.pub (What is GotitPub?)

Huggingface Toggle

Hugging Face (What is Huggingface?)

ScienceCast Toggle

ScienceCast (What is ScienceCast?)

Demos

Demos

Replicate Toggle

Replicate (What is Replicate?)

Spaces Toggle

Hugging Face Spaces (What is Spaces?)

Spaces Toggle

TXYZ.AI (What is TXYZ.AI?)

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower (What are Influence Flowers?)

Core recommender toggle

CORE Recommender (What is CORE?)

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |<br>Disable MathJax (What is MathJax?)