  We propose a novel generative model for time series based on Schr{\"o}dinger
bridge (SB) approach. This consists in the entropic interpolation via optimal
transport between a reference probability measure on path space and a target
measure consistent with the joint data distribution of the time series. The
solution is characterized by a stochastic differential equation on finite
horizon with a path-dependent drift function, hence respecting the temporal
dynamics of the time series distribution. We can estimate the drift function
from data samples either by kernel regression methods or with LSTM neural
networks, and the simulation of the SB diffusion yields new synthetic data
samples of the time series. The performance of our generative model is
evaluated through a series of numerical experiments. First, we test with a toy
autoregressive model, a GARCH Model, and the example of fractional Brownian
motion, and measure the accuracy of our algorithm with marginal and temporal
dependencies metrics. Next, we use our SB generated synthetic samples for the
application to deep hedging on real-data sets. Finally, we illustrate the SB
approach for generating sequence of images.
