TSFAdv: Frequency-Guided Black-Box Adversarial Attacks on Time Series Forecasting

Abstract

While deep neural network-based long-term time series forecasting (LTSF) has become indispensable for critical infrastructures such as smart grids and IoT platforms, the deployment of these models as black-box APIs introduces severe security vulnerabilities that remain largely underexplored. In this paper, we propose TSFAdv, a query-efficient adversarial framework for LTSF models. The framework systematically analyzes model sensitivity to spectral perturbations in both magnitude and phase of the frequency domain. By embedding frequency-domain priors into Natural Evolution Strategies, we achieve sensitivity-guided gradient estimation that improves perturbation efficacy without violating practical query constraints. To overcome ambiguities inherent to point-wise regression metrics, we adopt a trajectory-level evaluation protocol based on Dynamic Time Warping (DTW) and Slope Misalignment Error (SME), enabling the capture of complex geometric and directional deviations. Extensive experiments across seven state-of-the-art architectures demonstrate that TSFAdv achieves substantial performance gains, with average DTW improvements of 21.91–85.00% and SME improvements of 15.04–61.97% under a restrictive 200-query budget. These findings reveal that existing defense mechanisms are ineffective against frequency-domain manipulation, underscoring an urgent necessity for robust LTSF models; the code and artifacts are available at https:// anonymous.4open.science/r/TSFAdv.