Estimation and forecasting with logarithmic autoregressive conditional duration models: A comparative study with an application

This paper presents a semi-parametric method of parameter estimation for the class of logarithmic ACD (Log-ACD) models using the theory of estimating functions (EF). A number of theoretical results related to the corresponding EF estimators are derived. A simulation study is conducted to compare the performance of the proposed EF estimates with corresponding ML (maximum likelihood) and QML (quasi maximum likelihood) estimates. It is argued that the EF estimates are relatively easier to evaluate and have sampling properties comparable with those of ML and QML methods. Furthermore, the suggested EF estimates can be obtained without any knowledge of the distribution of errors is known. We apply all these suggested methodology for a real financial duration dataset. Our results show that Log-ACD (1, 1) fits the data well giving relatively smaller variation in forecast errors than in Linear ACD (1, 1) regardless of the method of estimation. In addition, the Diebold–Mariano (DM) and superior predictive ability (SPA) tests have been applied to confirm the performance of the suggested methodology. It is shown that the new method is slightly better than traditional methods in practice in terms of computation; however, there is no significant difference in forecasting ability for all models and methods.