  Inspired by the recent literature on aggregation theory, we aim at relating
the long range correlation of the stocks return volatility to the heterogeneity
of the investors' expectations about the level of the future volatility. Based
on a semi-parametric model of investors' anticipations, we make the connection
between the distributional properties of the heterogeneity parameters and the
auto-covariance/auto-correlation functions of the realized volatility. We
report different behaviors, or change of convention, whose observation depends
on the market phase under consideration. In particular, we report and justify
the fact that the volatility exhibits significantly longer memory during the
phases of speculative bubble than during the phase of recovery following the
collapse of a speculative bubble.
