A Comment on: “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data”

IF 6.6 1区经济学 Q1 ECONOMICS

Econometrica Pub Date : 2025-03-29 DOI:10.3982/ECTA21896

Giuseppe Cavaliere, Thomas Mikosch, Anders Rahbek, Frederik Vilandt

引用次数: 0

Abstract

Based on the GARCH literature, Engle and Russell (1998) established consistency and asymptotic normality of the QMLE for the autoregressive conditional duration (ACD) model, assuming strict stationarity and ergodicity of the durations. Using novel arguments based on renewal process theory, we show that their results hold under the stronger requirement that durations have finite expectation. However, we demonstrate that this is not always the case under the assumption of stationary and ergodic durations. Specifically, we provide a counterexample where the MLE is asymptotically mixed normal and converges at a rate significantly slower than usual. The main difference between ACD and GARCH asymptotics is that the former must account for the number of durations in a given time span being random. As a by-product, we present a new lemma which can be applied to analyze asymptotic properties of extremum estimators when the number of observations is random.

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基于 GARCH 文献，Engle 和 Russell（1998 年）建立了自回归条件持续时间（ACD）模型的 QMLE 一致性和渐近正态性，假设持续时间具有严格的静止性和遍历性。我们利用基于更新过程理论的新颖论证，证明了在持续时间具有有限期望这一更高要求下，他们的结果是成立的。然而，我们证明，在持续时间具有静止性和遍历性的假设条件下，情况并非总是如此。具体来说，我们提供了一个反例，在这个反例中，MLE 是渐近混合正态分布，收敛速度比通常情况下慢得多。ACD 与 GARCH 渐进式的主要区别在于，前者必须考虑到给定时间跨度内的持续时间数量是随机的。作为副产品，我们提出了一个新的 Lemma，可用于分析观测值数量随机时极值估计器的渐近特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Econometrica 社会科学-数学跨学科应用

CiteScore

11.00

自引率

3.30%

发文量

审稿时长

6-12 weeks

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