A (Semi)Parametric Functional Coefficient Logarithmic Autoregressive Conditional Duration Model

Abstract

In this article, we propose a class of logarithmic autoregressive conditional duration (ACD)-type models that accommodates overdispersion, intermittent dynamics, multiple regimes, and asymmetries in financial durations. In particular, our functional coefficient logarithmic autoregressive conditional duration (FC-LACD) model relies on a smooth-transition autoregressive specification. The motivation lies on the fact that the latter yields a universal approximation if one lets the number of regimes grows without bound. After establishing sufficient conditions for strict stationarity, we address model identifiability as well as the asymptotic properties of the quasi-maximum likelihood (QML) estimator for the FC-LACD model with a fixed number of regimes. In addition, we also discuss how to consistently estimate a semiparametric variant of the FC-LACD model that takes the number of regimes to infinity. An empirical illustration indicates that our functional coefficient model is flexible enough to model IBM price durations.

Keywords:

• Explosive regimes
• Neural networks
• Quasi-maximum likelihood
• Sieve estimation
• Smooth transition
• Stationarity

JEL Classification:

• C22

ACKNOWLEDGEMENTS

We are grateful to Essie Maasoumi (editor) and an anonymous referee for their constructive comments. We are also indebted to Valentina Corradi, Emmanuel Guerre, Oliver Linton, José António Ferreira Machado, Olivier Scaillet, and Howell Tong for helpful discussions as well as to seminar participants at Queen Mary, SoFiE European Conference (Geneva, Switzerland), Encontro Brasileiro de Econometria (Natal, Brazil), 50 Years of the Econometric Institute (Rotterdam, The Netherlands), Nonlinear Dynamical Methods and Time Series Analysis (Udine, Italy), and Econometrics in Rio (Rio de Janeiro, Brazil) for valuable comments. The usual disclaimer applies.