Simulation of non-stationary event flow with a nested stationary component

A method for constructing an ensemble of time series trajectories with a nonstationary flow of events and a non-stationary empirical distribution of the values of the observed random variable is described. We consider a special model that is similar in properties to some real processes, such as changes in the price of a financial instrument on the exchange. It is assumed that a random process is represented as an attachment of two processes - stationary and non-stationary. That is, the length of a series of elements in the sequence of the most likely event (the most likely price change in the sequence of transactions) forms a non-stationary time series, and the length of a series of other events is a stationary random process. It is considered that the flow of events is non-stationary Poisson process. A software package that solves the problem of modeling an ensemble of trajectories of an observed random variable is described. Both the values of a random variable and the time of occurrence of the event are modeled. An example of practical application of the model is given.