发表机构
Department of Economics, University of Bologna; Department of Economics, University of Exeter; Department of Economics, University of Copenhagen（博洛尼亚大学经济系; 埃克塞特大学经济系; 哥本哈根大学经济系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对固定日历跨度内观测的自回归条件持续期（ACD）模型开发自助推断方法，固定数量自助法在不同尾指数条件下具有良好性质，蒙特卡洛实验验证其有效性，应用于加密货币ETF交易持续期体现了实际价值。
AI 中文摘要
本文针对在固定日历跨度内观测到的自回归条件持续期（ACD）模型，开发了自助推断方法，其中持续期的数量是随机的。我们研究了要么固定日历跨度、要么固定已实现事件数量的递归方案。对于固定数量自助法，当持续期尾指数满足κ≥1时，我们建立了其一致性；当0<κ<1时，经典一致性失效，因为估计量具有混合正态极限，但自助法能重现其条件高斯分量。因此，基本百分位区间仍具有一阶有效性，自助t统计量渐近服从标准正态分布。蒙特卡洛实验表明，该方法在有限均值和无限均值机制下均能实现准确的有限样本推断，且对非指数 innovations 具有鲁棒性。将其应用于加密货币ETF交易持续期，发现了强持续性，并说明了固定数量与随机数量推断之间的实际差异。
英文摘要
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.
