Learning to Simulate Sequentially Generated Data via Neural Networks and Wasserstein Training

We propose a new framework of a neural network-assisted sequential structured simulator to model, estimate, and simulate a wide class of sequentially generated data. Neural networks are integrated into the sequentially structured simulators in order to capture potential nonlinear and complicated sequential structures. Given representative real data, the neural network parameters in the simulator are estimated through a Wasserstein training process, without restrictive distributional assumptions. Moreover, the simulator can flexibly incorporate various kinds of elementary randomness and generate distributions with certain properties such as heavy-tail. Regarding statistical properties, we provide results on consistency and convergence rate for estimation of the simulator. We then present numerical experiments with synthetic and real data sets to illustrate the performance of our estimation method.