*Article* **A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data**

#### **Danúbia R. Cunha 1, Roberto Vila 2, Helton Saulo 2,\* and Rodrigo N. Fernandez 3**


Received: 24 December 2019; Accepted: 26 February 2020; Published: 3 March 2020

**Abstract:** In this paper, we propose a general family of Birnbaum–Saunders autoregressive conditional duration (BS-ACD) models based on generalized Birnbaum–Saunders (GBS) distributions, denoted by GBS-ACD. We further generalize these GBS-ACD models by using a Box-Cox transformation with a shape parameter *λ* to the conditional median dynamics and an asymmetric response to shocks; this is denoted by GBS-AACD. We then carry out a Monte Carlo simulation study to evaluate the performance of the GBS-ACD models. Finally, an illustration of the proposed models is made by using New York stock exchange (NYSE) transaction data.

**Keywords:** generalized Birnbaum–Saunders distributions; ACD models; Box-Cox transformation; high-frequency financial data; goodness-of-fit

**MSC:** Primary 62P20; Secondary 62F99

**JEL Classification:** Primary C51; Secondary C52 C53
