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Title: Asymptotics and inference for autoregressive conditional duration models Authors:  Giuseppe Cavaliere - University of Bologna (Italy)
Thomas Mikosch - University of Copenhagen (Denmark)
Anders Rahbek - University of Copenhagen (Denmark) [presenting]
Frederik Vilandt - (Denmark)
Abstract: New asymptotic distributional results are presented for likelihood-based estimators in autoregressive conditional duration (ACD) models. We show the unexpected result that the large sample behavior of the estimators strongly depends on the tail behavior of the duration data, and hence on the finiteness of moments. In particular, we show that asymptotic normality breaks down when the tail index of the durations is smaller than one. In this case, the estimators are shown to be asymptotically mixed Gaussian with a non-standard rate of convergence depending on the tail index. Our results are particularly surprising when compared to the analysis of ARCH models: while ARCH and ACD likelihood functions have the same form, standard asymptotic arguments apply to ARCH models but not to ACD models. The crucial difference between the two types of models is that for ACD models, the number of observations within any given sample period is random. This feature, rather than being innocuous, requires as demonstrated new, non-standard theory.