A neural network approach for simulating stationary stochastic processes

In this paper a procedure for Monte Carlo simulation of univariate stationary stochastic processes with the aid of neural networks is presented. Neural networks operate model-free and, thus, circumvent the need of specifying a priori statistical properties of the process, as needed traditionally. This is particularly advantageous when only limited data are available. A neural network can capture the "pattern" of a short observed time series. Afterwards, it can directly generate stochastic process realizations which capture the properties of the underlying data. In the present study a simple feedforward network with focused time-memory is utilized. The proposed procedure is demonstrated by examples of Monte Carlo simulation, by synthesis of future values of an initially short single process record.