What the study found
The study found evidence of infinite-mean durations in all five cryptocurrency ETF markets examined. It also found that the integrated 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 whether durations between trades have finite or infinite expectation, which is described as a key empirical question in duration models. They also note that finite expectation is often assumed implicitly in point process models, and their findings indicate that assumption does not hold in their data.
What the researchers tested
The researchers developed a unified asymptotic theory for the quasi-maximum likelihood estimator in integrated autoregressive conditional duration (ACD) models, which are counterparts to integrated generalized autoregressive conditional heteroskedastic models used for financial returns. They then used the new theoretical results to build a hypothesis-testing framework and applied it to high-frequency cryptocurrency ETF trading data.
What worked and what didn't
The new theory filled a gap in asymptotic theory for ACD models, according to the abstract. In the empirical application, infinite-mean durations were found for all five ETFs, and the integrated ACD hypothesis was rejected for four of the five ETFs; the abstract does not report additional performance measures.
What to keep in mind
The abstract does not describe specific limitations beyond noting that asymptotic theory for ACD had been incomplete before this work. The empirical findings are limited to the five cryptocurrency ETFs studied.
Key points
- All five cryptocurrency ETFs examined showed evidence of infinite-mean durations.
- The integrated ACD hypothesis was rejected for four of the five ETFs.
- The authors developed a unified asymptotic theory for quasi-maximum likelihood estimation in integrated ACD models.
- A new hypothesis-testing framework was introduced to test whether durations have finite or infinite expectation.
- The empirical analysis used high-frequency cryptocurrency ETF trading data.
Disclosure
- Research title:
- Integrated ACD models can imply infinite-mean durations
- Authors:
- Giuseppe Cavaliere, Thomas Mikosch, Anders Rahbek, Frederik Vilandt
- Publication date:
- 2026-03-30
- OpenAlex record:
- View
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