Bootstrapping autoregressive duration models
Abstract
This paper develops bootstrap methods for likelihood-based inference in autoregressive conditional duration (ACD) models, where the sample size is endogenously determined by durations observed over a fixed time span. This feature fundamentally shapes the asymptotic framework, particularly so when the durations do not have finite expectation. Building on recent limit theory for heavy-tailed and integrated ACD processes, we analyze recursive bootstrap schemes that either fix the time span (yielding a random sample size) or fix the number of durations (yielding a random time span). We establish a bootstrap theory for ACD models that links naturally to renewal theory with random sample sizes. For the fixedcount bootstrap, we prove first-order validity in the finite-mean and boundary cases and characterize the random limiting bootstrap distribution in the infinite-mean case. Although classical bootstrap consistency can fail when the durations have infinite expectation, we argue that the bootstrap remains valid and yields asymptotically normal t-statistics. Monte Carlo evidence shows that the proposed methods have good finite-sample properties in both finite- and infinite-mean settings, and are robust to distributional misspecification relative to the exponential likelihood. We conclude with an empirical application to cryptocurrency ETFs.
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BibTeX
@misc{cavaliere2026bootstrapping,
title = {{Bootstrapping autoregressive duration models}},
author = {Giuseppe Cavaliere and Anders Rahbek and Frederik Vilandt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.28294},
eprint = {2607.28294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28294},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bootstrapping autoregressive duration models
AU - Giuseppe Cavaliere
AU - Anders Rahbek
AU - Frederik Vilandt
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.28294
UR - https://arxiv.org/abs/2607.28294
AB - This paper develops bootstrap methods for likelihood-based inference in autoregressive conditional duration (ACD) models, where the sample size is endogenously determined by durations observed over a fixed time span. This feature fundamentally shapes the asymptotic framework, particularly so when the durations do not have finite expectation. Building on recent limit theory for heavy-tailed and integrated ACD processes, we analyze recursive bootstrap schemes that either fix the time span (yielding a random sample size) or fix the number of durations (yielding a random time span). We establish a bootstrap theory for ACD models that links naturally to renewal theory with random sample sizes. For the fixedcount bootstrap, we prove first-order validity in the finite-mean and boundary cases and characterize the random limiting bootstrap distribution in the infinite-mean case. Although classical bootstrap consistency can fail when the durations have infinite expectation, we argue that the bootstrap remains valid and yields asymptotically normal t-statistics. Monte Carlo evidence shows that the proposed methods have good finite-sample properties in both finite- and infinite-mean settings, and are robust to distributional misspecification relative to the exponential likelihood. We conclude with an empirical application to cryptocurrency ETFs.
ER -