Simple stochastic simulation of time irreversible and reversible processes

As time irreversibility of streamflow is marked for time scales up to several days, while common stochastic generation methods are good only for time-symmetric processes, the need for new methods to handle irreversibility, particularly in flood simulations, has been recently highlighted. From an investigation of the historical evolution of existing stochastic generation methods, which is a useful step before proposing new methods, the strengths and weaknesses of current approaches are located. Following this investigation, a generic solution to the stochastic generation problem is proposed. This is an analytical exact method based on an asymmetric moving-average scheme, capable of handling time irreversibility in addition to preserving the second-order stochastic structure, as well as higher-order marginal statistics, of a process. The method is studied theoretically in its general setting, as well as in its most interesting special cases, and is successfully applied to streamflow generation at an hourly scale.