Tail Behavior of ACD Models and Consequences for Likelihood-Based Estimation
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Tail Behavior of ACD Models and Consequences for Likelihood-Based Estimation. / Cavaliere, Giuseppe; Mikosch, Thomas Valentin; Rahbek, Anders; Rasmussen, Frederik Vilandt.
In: Journal of Econometrics, Vol. 238, No. 2, 105613, 2024.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Tail Behavior of ACD Models and Consequences for Likelihood-Based Estimation
AU - Cavaliere, Giuseppe
AU - Mikosch, Thomas Valentin
AU - Rahbek, Anders
AU - Rasmussen, Frederik Vilandt
PY - 2024
Y1 - 2024
N2 - 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), 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 behavior 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.
AB - 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), 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 behavior 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.
U2 - 10.1016/j.jeconom.2023.105613
DO - 10.1016/j.jeconom.2023.105613
M3 - Journal article
VL - 238
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 2
M1 - 105613
ER -
ID: 369492054