arXiv subjects

Frederik Vilandt

Publications and source records attributed to Frederik Vilandt.

4 recordsLinked to original sources

arXiv2026

Bootstrap inference in autoregressive duration models

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.

econ.EM↗

arXiv2025

Beyond the Mean: Limit Theory and Tests for Infinite-Mean Autoregressive Conditional Durations

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.

econ.EM↗

arXiv2023

Asymptotics for the Generalized Autoregressive Conditional Duration Model

Engle and Russell (1998, Econometrica, 66:1127--1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarity and ergodicity. The GARCH results, however, do not account for the fact that the number of durations over a given observation period is random. Thus, in contrast with Engle and Russell (1998), we show that strict stationarity and ergodicity alone are not sufficient for consistency and asymptotic normality, and provide additional sufficient conditions to account for the random number of durations. In particular, we argue that the durations need to satisfy the stronger requirement that they have finite mean.

econ.EM↗

arXiv2022

The Econometrics of Financial Duration Modeling

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998, Econometrica 66, 1127-1162), we show that the large sample behavior of likelihood estimators is highly sensitive to the tail behavior of the financial durations. In particular, even under stationarity, asymptotic normality breaks down for tail indices smaller than one or, equivalently, when the clustering behaviour of the observed events is such that the unconditional distribution of the durations has no finite mean. Instead, we find that estimators are mixed Gaussian and have non-standard rates of convergence. The results are based on exploiting the crucial fact that for duration data the number of observations within any given time span is random. Our results apply to general econometric models where the number of observed events is random.

econ.EM↗