STOCHASTIC TIME CHANGE, VOLATILITY, AND NORMALITY OF RETURNS: A HIGH-FREQUENCY DATA ANALYSIS WITH A SAMPLE OF LSE STOCKS

Abstract

The purpose of this chapter is to verify whether the stochastic time change leading to a Gaussian representation of the conditional asset returns density is best represented by the number of trades. We use the same procedure then on Ane and Geman (2000) to estimate the four first moments of the latent stochastic time change/information flow that permits to recover the normality of stock returns, using a sample of LSE highly traded stocks. We are able to show empirically that the moments greater than one of the stochastic time changes coincide virtually with the moments of the number of trades. Then, we recenter the number of trades so as to have the same mean than the stochastic time change. The distribution of returns conditioned on the recentered number of trades does not correspond to the normal case. We argue that, in our data, the choice of the cumulative number of trades to represent the economic clock is not adequate. Finally, we explain why we find such results which are in line with recent empirical findings, in particular Murphy and Izzeldin (2005) and Gillemot et al. (2005).