Nonparametric generative modeling for time series via Schrödinger bridge

Mohamed Hamdouche (), Pierre Henry-Labordere () and Huyên Pham ()
Additional contact information
Mohamed Hamdouche: Qube Research and Technologies
Pierre Henry-Labordere: Qube Research and Technologies
Huyên Pham: X - École polytechnique - IP Paris - Institut Polytechnique de Paris, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

Working Papers from HAL

Abstract: We propose a novel generative model for time series based on Schr\"odinger 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 respec\-ting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, 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 autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.

Keywords: generative models; time series; Schrödinger bridge; kernel estimation; deep hedging (search for similar items in EconPapers)
Date: 2026-04-01
New Economics Papers: this item is included in nep-big, nep-des, nep-ecm and nep-ets
Note: View the original document on HAL open archive server: https://hal.science/hal-04063041v2
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Ecole Polytechnique (Palaiseau, France). 2026

Downloads: (external link)
https://hal.science/hal-04063041v2/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04063041

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().