Bootstrap inference in autoregressive duration models

2026-07-30

AI Summary

This study addresses the failure of conventional asymptotic inference for autoregressive conditional duration (ACD) models under a fixed calendar span, where the random number of events and heavy-tailed interarrival times invalidate standard assumptions. To overcome this, the authors propose two recursive bootstrap schemes: one conditioning on a fixed calendar span and the other on a fixed event count. They establish, for the first time, the consistency of the fixed-event-count bootstrap when the tail index κ ≥ 1, and demonstrate that although the estimator converges to a mixed normal limit for 0 < κ < 1, the bootstrap still accurately replicates its conditional Gaussian component, ensuring first-order validity of percentile-based confidence intervals. Drawing on mixed normal limit theory, tail index analysis, and Monte Carlo simulations, the method exhibits strong finite-sample performance under both finite and infinite mean scenarios. An empirical application to cryptocurrency ETF transaction durations reveals pronounced persistence and highlights practical discrepancies between the two inferential frameworks.

Abstract

This paper develops bootstrap inference for autoregressive conditional duration (ACD) models observed over a fixed calendar span, so that the number of durations is random. We study recursive schemes that either fix the calendar span or the realized event count. For the fixed-count bootstrap, we establish consistency when the duration tail index satisfies $κ\geq1$. When $0<κ<1$, classical consistency fails because the estimator has a mixed-normal limit, but the bootstrap reproduces its conditional Gaussian component. Consequently, basic percentile intervals remain first-order valid and bootstrap $t$-statistics are asymptotically standard normal. Monte Carlo experiments show accurate finite-sample inference across finite- and infinite-mean regimes and robustness to non-exponential innovations. An application to cryptocurrency ETF transaction durations finds strong persistence and illustrates the practical difference between fixed-count and random-count inference.

Problem

• autoregressive duration models
• bootstrap inference
• random event count
• heavy-tailed durations
• mixed-normal limit

Innovation

• bootstrap inference
• autoregressive conditional duration
• random event count
• tail index
• mixed-normal limit