Time Series Simulation

Nested Optimal Transport Distances ArXiv ID: 2509.06702 “View on arXiv” Authors: Ruben Bontorno, Songyan Hou Abstract Simulating realistic financial time series is essential for stress testing, scenario generation, and decision-making under uncertainty. Despite advances in deep generative models, there is no consensus metric for their evaluation. We focus on generative AI for financial time series in decision-making applications and employ the nested optimal transport distance, a time-causal variant of optimal transport distance, which is robust to tasks such as hedging, optimal stopping, and reinforcement learning. Moreover, we propose a statistically consistent, naturally parallelizable algorithm for its computation, achieving substantial speedups over existing approaches. ...

ProteuS: A Generative Approach for Simulating Concept Drift in Financial Markets ArXiv ID: 2509.11844 “View on arXiv” Authors: Andrés L. Suárez-Cetrulo, Alejandro Cervantes, David Quintana Abstract Financial markets are complex, non-stationary systems where the underlying data distributions can shift over time, a phenomenon known as regime changes, as well as concept drift in the machine learning literature. These shifts, often triggered by major economic events, pose a significant challenge for traditional statistical and machine learning models. A fundamental problem in developing and validating adaptive algorithms is the lack of a ground truth in real-world financial data, making it difficult to evaluate a model’s ability to detect and recover from these drifts. This paper addresses this challenge by introducing a novel framework, named ProteuS, for generating semi-synthetic financial time series with pre-defined structural breaks. Our methodology involves fitting ARMA-GARCH models to real-world ETF data to capture distinct market regimes, and then simulating realistic, gradual, and abrupt transitions between them. The resulting datasets, which include a comprehensive set of technical indicators, provide a controlled environment with a known ground truth of regime changes. An analysis of the generated data confirms the complexity of the task, revealing significant overlap between the different market states. We aim to provide the research community with a tool for the rigorous evaluation of concept drift detection and adaptation mechanisms, paving the way for more robust financial forecasting models. ...