**7. Concluding Remarks**

We have introduced a general class of ACD models based on GBS distributions. These distributions possess either lighter or heavier tails than the BS distribution, thus providing a wider class of positively skewed densities with nonnegative support. In addition, we have proposed a

wider class of GBS-ACD models based on the Box-Cox transformation with a shape parameter to the conditional duration process and an asymmetric response to shocks. We then investigated the performance of the maximum likelihood estimates of the GBS-ACD models by means of an MC study. We also compared the proposed GBS-ACD and GBS-AACD models through an analysis with real financial data sets, which has shown the superiority of the BS-PE-ACD and BS-PE-BCACD models. A future line of research may be the out-of-sample forecast abilities of these models, as well as their application to other types of irregularly time-spaced data (besides TD data).

**Author Contributions:** All authors contributed equally to this manuscript. All authors have read and agreed to the published version of the manuscript

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
