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Infinite-mean durations found in five cryptocurrency ETFs

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A close-up view of a digital financial trading screen displaying multiple colorful line charts in red, green, and yellow against a dark blue background, with a blurred trading interface and data visualizations visible in the foreground.
Research area:Economics, Econometrics and FinanceFinanceAutoregressive model

What the study found

The study found evidence of infinite-mean durations, meaning the average time between trades may not be finite, in five cryptocurrency exchange traded funds (ETFs). The authors also report that the integrated autoregressive conditional duration (ACD) hypothesis was rejected for four of the five ETFs in favor of heavier-tailed alternatives.

Why the authors say this matters

The authors say their results address a key empirical question in duration models: whether trade durations have a finite or infinite expectation. They also note that this is an assumption often made implicitly in point process models.

What the researchers tested

The researchers developed a unified asymptotic theory for the quasi-maximum likelihood estimator in integrated ACD models. They also proposed a new hypothesis-testing framework for duration models and applied it to high-frequency cryptocurrency ETF trading data.

What worked and what didn't

The new theory was used to support inference in integrated ACD models, where conventional asymptotic approaches break down because the number of durations in a fixed observation period is random. In the empirical application, the findings indicate infinite-mean durations for all five cryptocurrency ETFs, and the integrated ACD hypothesis was rejected for four of them.

What to keep in mind

The abstract does not describe detailed limitations beyond noting that asymptotic theory for ACD has been incomplete and that standard asymptotic methods break down in this setting. The empirical results are reported for five cryptocurrency ETFs only.

Key points

  • The paper develops asymptotic theory for integrated autoregressive conditional duration (ACD) models.
  • It introduces a hypothesis-testing framework for deciding whether durations have finite or infinite expectation.
  • In five cryptocurrency ETFs, the authors find evidence of infinite-mean trade durations.
  • The integrated ACD hypothesis is rejected for four of the five ETFs in favor of heavier-tailed alternatives.
  • The study focuses on high-frequency trading data from cryptocurrency ETFs.

Disclosure

Research title:
Infinite-mean durations found in five cryptocurrency ETFs
Authors:
Giuseppe Cavaliere, Thomas Mikosch, Anders Rahbek, Frederik Vilandt
Institutions:
Department of Mathematical Sciences, GNA University, IT University of Copenhagen, IT University of Copenhagen, University College Copenhagen, University College Copenhagen, University of Bologna, University of Copenhagen, University of Copenhagen, University of Copenhagen, University of Exeter
Publication date:
2026-03-30
DOI:
10.1093/jrsssb/qkag053
OpenAlex record:
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AI provenance: This post was generated by gpt-5.4-mini (OpenAI). The original authors did not write or review this post.