Bootstrap Inference for Autoregressive Conditional Duration Models

Summary

The paper develops bootstrap procedures for likelihood-based inference in autoregressive conditional duration models. Because observations are durations recorded over a fixed span of time, the number of observations can be random; the asymptotic behavior also changes when durations have infinite expectation. The authors study two recursive bootstrap designs: one holds the time span fixed, and the other fixes the duration count while allowing the span to vary.

The theory connects the procedures to renewal processes with random sample sizes. For the fixed-count design, the paper establishes first-order validity in finite-mean and boundary cases and describes the random limiting bootstrap distribution in the infinite-mean case. It argues that t-statistics can remain asymptotically normal even where classical bootstrap consistency fails. Monte Carlo evidence is reported for finite- and infinite-mean settings, including robustness to misspecification relative to an exponential likelihood, and the paper includes an application to cryptocurrency ETFs. The abstract does not give detailed simulation settings or application results.

Key ideas

• ACD bootstrap inference must account for sample size being determined by durations over a time span.
• The paper compares bootstraps that fix the observation window with those that fix the duration count.
• Infinite-mean durations can produce a random limiting bootstrap distribution and challenge classical consistency.
• The authors report asymptotically normal t-statistics and favorable finite-sample simulation properties.
• An empirical application examines cryptocurrency ETFs.

Tags

# Bootstrapping autoregressive duration models


# Bootstrapping autoregressive duration models









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.