Recovering the moments of information flow and the normality of asset returns

We investigate the univariate procedure used by Ane and Geman (AG, 2000) to recover the moments of the information flow from high-frequency data, in a mixture of distributions model which generalizes the subordinated process in Clark (1973). We explain why the third and higher moments of the latent information flow cannot be accurately recovered using this procedure. We illustrate this using Monte Carlo simulations. We also show that, contrary to the claims in AG, returns conditioned on the re-centred number of trades are not approximately Gaussian. Finally, we consider the bivariate approach of Richardson and Smith (1994), inter alia, to recover the moments of information flow.