Order flow, transaction clock, and normality of asset returns

The goal of this paper is to show that normality of asset returns can be re covered through a stochastic time change. Clark (1973) addressed this issue by representing the price process as a subordinated process with volume as the lognormally distributed subordinator. We extend Clark's results and fi nd the following: (i) stochastic time chang-es are mathematically much less constraining than subordinators; (ii) the cumulative number of trades is a better stochastic clock than the volume for generating virtually perfect n ormality in returns; (iii) this clock can be modeled nonparametrically, all owing both the time-change and price processes to take the form of jump dif fusions.