What the study found
The study found evidence of infinite-mean durations, meaning the average time between trades may not be finite, in all five cryptocurrency exchange traded funds (ETFs) they examined. The authors also report rejecting the integrated autoregressive conditional duration (ACD) hypothesis for four of the five ETFs in favor of heavier-tailed alternatives.
Why the authors say this matters
The authors say their results address whether durations between trades have a finite or infinite expectation, which they describe as a key empirical question in duration models. They also note that a finite expectation is often assumed implicitly in the point process literature.
What the researchers tested
The paper develops a unified asymptotic theory for the quasi-maximum likelihood estimator in integrated ACD models, which are models for time between events. The authors then use the new theory to build hypothesis tests for whether durations have finite or infinite expectation, and apply the framework to high-frequency cryptocurrency ETF trading data.
What worked and what didn't
The new theoretical results support inference in integrated ACD models despite the complication that 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 is rejected for four of them in favor of heavier-tailed alternatives.
What to keep in mind
The abstract does not describe detailed limitations beyond the theoretical challenges the authors address. The empirical results are specific to the five cryptocurrency ETFs studied, so the abstract does not claim they apply more broadly.
Key points
- The paper provides asymptotic theory for integrated ACD models.
- It introduces tests for whether durations have finite or infinite expectation.
- All five cryptocurrency ETFs studied showed evidence of infinite-mean durations.
- The integrated ACD hypothesis was rejected for four of the five ETFs.
- The authors report heavier-tailed alternatives fit better for four 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
- OpenAlex record:
- View
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