Before revision:  The time-varying feature of the PHE allows us to apply such class of multifractional processes to model stock prices under various market conditions, that are both time-dependent and region-dependent.
After revision:  Such multifractional processes, whose PHEs are time-varying feature of the PHE allows us to apply such class of multifractional processes to model stock prices under various market conditions, that are both time-dependent and region-dependent.