Simulation of Historical Time Series Using MPRE, a Focus on Correlation in Squared Returns

In this work, assuming as a model of price dynamic the Multifractional Processes with Random Exponent (MPRE), we analyze the behaviour of simulated time series in terms of autocorrelation. We show how, properly choosing the random exponent of MPRE, it is possible to capture the slow decay of autocorrelation of squared returns by preserving the absence of correlation in returns. The empirical analysis spotlights that a probable link between the previous two stylized facts and the fair behaviour of MPRE in their replication seems to be the continuity of the random exponent.