Financial durations models are widely used in finance to model the time between events such as trades, stock price movements, or other financial events. A workhorse in the literature is the classical autoregressive conditional duration (ACD) models by Engle and Russell (Econometrica, 1998), where the expected conditional duration depends on the most recent past durations. The likelihood of the model resembles the Gaussian (G)ARCH likelihood, and it is widely believed that asymptotic results for conditional volatility models carry over to ACD models. In this talk I will show that this common wisdom is generally incorrect, and that the asymptotic theory for ACD is actually non-standard and requires different machinery. Specifically, I will show that the behavior of likelihood estimators in ACD models is highly sensitive to the tail behavior of the financial durations: asymptotic normality breaks down when the tail indices of the durations are smaller than unity, and estimators are mixed Gaussian with non-standard rates of convergence. These results are based on exploiting the fact that the number of observations within any given time span is random for duration data. I will discuss the implications of these results for financial durations modeling and inference, and provide some examples in real-world settings.
Giuseppe Cavaliere is Full Professor of Econometrics at the University of Bologna (since 2006) and Distinguished Research Professor of Economics at the Exeter Business School. He has been affiliated with professorships at the University of Copenhagen and University of Aarhus. He is also Elected Fellow of the International Association for Applied Econometrics (IAAE), Fellow of the Journal of Econometrics and Research Fellow of the Granger Centre for Time Series Econometrics (University of Nottingham). He has acted as president of the Italian Econometric Association (SIdE). He has published in several international top journals, including Econometrica, the Annals of Statistics, the Journal of the American Statistical Association, Econometric Theory and the Journal of Econometrics. He is a co-editor of Econometric Theory and associate editor of the Journal of Econometrics, the Econometrics Journal and the Journal of Time Series Analysis.