A Theoretical Analysis of Detecting Large Model-Generated Time Series

TL;DR

This paper introduces a theoretical framework and a new detection method for identifying large model-generated time series by leveraging the uncertainty contraction phenomenon under recursive forecasting.

Contribution

It proposes the contraction hypothesis and the Uncertainty Contraction Estimator (UCE), a novel white-box detector that outperforms existing methods in identifying synthetic time series.

Findings

UCE outperforms state-of-the-art baselines across 32 datasets.

Model-generated time series show decreasing uncertainty under recursive forecasting.

The contraction hypothesis is validated both theoretically and empirically.

Abstract

Motivated by the increasing risks of data misuse and fabrication, we investigate the problem of identifying synthetic time series generated by Time-Series Large Models (TSLMs) in this work. While there are extensive researches on detecting model generated text, we find that these existing methods are not applicable to time series data due to the fundamental modality difference, as time series usually have lower information density and smoother probability distributions than text data, which limit the discriminative power of token-based detectors. To address this issue, we examine the subtle distributional differences between real and model-generated time series and propose the contraction hypothesis, which states that model-generated time series, unlike real ones, exhibit progressively decreasing uncertainty under recursive forecasting. We formally prove this hypothesis under theoretical assumptions on model behavior and time series structure. Model-generated time series exhibit progressively concentrated distributions under recursive forecasting, leading to uncertainty contraction. We provide empirical validation of the hypothesis across diverse datasets. Building on this insight, we introduce the Uncertainty Contraction Estimator (UCE), a white-box detector that aggregates uncertainty metrics over successive prefixes to identify TSLM-generated time series. Extensive experiments on 32 datasets show that UCE consistently outperforms state-of-the-art baselines, offering a reliable and generalizable solution for detecting model-generated time series.