Beyond the Mean: Limit Theory and Tests for Infinite-Mean Autoregressive Conditional Durations
超越均值：无限均值自回归条件持续期模型的极限理论与检验AI 解读 ↓
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超越均值：无限均值自回归条件持续期模型的极限理论与检验
- 研究问题
- 在固定观察窗口内交易次数随机、持续期可能没有有限均值时，如何建立 ACD 参数估计的极限理论，并检验均值是否有限？
- 方法与思路
- 作者为 ACD 模型的拟极大似然估计建立包含整合情形的统一渐近理论，据此构造持续期假设检验，并应用于高频交易数据。
- 材料陈述的贡献
- 摘要称该理论覆盖整合 ACD；五种加密资产的交易持续期均呈无限均值证据，其中四种拒绝整合假设而支持尾指数小于一的备择。
- 阅读关注点
- 应核对随机交易次数如何进入极限理论、整合边界与尾指数的关系，以及检验假设、数据处理和无限均值证据的解释。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收状态未核实。摘要未说明正则条件、极限分布及检验数值，不能据此推广到其他市场。
原文摘要
Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and also not complete, in particular for integrated ACD. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation, and (ii) even in the non-integrated case, conventional asymptotic approaches break down due to the randomness in the number of durations within a fixed observation period. Addressing these challenges, we provide here unified asymptotic theory for the (quasi-) maximum likelihood estimator for ACD models; a unified theory which includes integrated ACD models. Based on the new results, we also provide a novel framework for hypothesis testing in duration models, enabling inference on a key empirical question: whether durations possess a finite or infinite expectation. We apply our results to high-frequency cryptocurrency ETF trading data. Motivated by parameter estimates near the integrated ACD boundary, we assess whether durations between trades in these markets have finite expectation, an assumption often made implicitly in the literature on point process models. Our empirical findings indicate infinite-mean durations for all the five cryptocurrencies examined, with the integrated ACD hypothesis rejected -- against alternatives with tail index less than one -- for four out of the five cryptocurrencies considered.