Before revision:  Second, we develop a structured and parsimonious model of clock-time returns by subordinating a trade-time Gaussian distribution with a trade arrival process that is associated with a modified Markov-Switching Multifractal Duration (MSMD) model of Chen et al. (2013). Our modification of the MSMD model provides a much better characterization of high-frequency inter-trade durations than the original model of Chen et al. (2013).
After revision:  Second, we develop a structured and parsimonious model of clock-time returns by subordinating a trade-time Gaussian distribution with a trade arrival process that is associated with a modified Markov-Switching Multifractal Duration (MSMD) model . This model provides an excellent characterization of high-frequency inter-trade durations than the original model of Chen et al. (2013).