  We present a simple microstructure model of financial returns that combines
(i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the
bid-ask bounce effect, (iii) the fat tail structure of the distribution of
returns and (iv) the non-Poissonian statistics of inter-trade intervals. This
model allows us to explain both qualitatively and quantitatively important
stylized facts observed in the statistics of microstructure returns, including
the short-ranged correlation of returns, the long-ranged correlations of
absolute returns, the microstructure noise and Epps effects. According to the
microstructure noise effect, volatility is a decreasing function of the time
scale used to estimate it. Paradoxically, the Epps effect states that cross
correlations between asset returns are increasing functions of the time scale
at which the returns are estimated. The microstructure noise is explained as
the result of the negative return correlations inherent in the definition of
the bid-ask bounce component (ii). In the presence of a genuine correlation
between the returns of two assets, the Epps effect is due to an average
statistical overlap of the momentum of the returns of the two assets defined
over a finite time scale in the presence of the long memory process (i).
