Differentially Private Time Series Data Publishing via STL Decomposition and Adaptive Budget Allocation

Time series data is integral to numerous applications, but its sensitive nature necessitates privacy-preserving publication mechanisms. This paper proposes a novel framework for publishing differentially private time series data. The core idea involves decomposing the time series into trend, seasonal, and residual components using Seasonal and Trend decomposition using Loess (STL). The trend component is smoothed using a sliding window average, and noise is added according to the Laplace mechanism to ensure differential privacy. The seasonal component is perturbed using the Fourier Perturbation Algorithm (FPA). A key aspect of our approach is the adaptive allocation of the overall privacy budget between the trend and seasonal components based on their respective information content. This strategy aims to optimize the utility of the published data while maintaining rigorous privacy guarantees. We provide a detailed description of the methodology, including sensitivity analysis for each component and the budget allocation mechanism. Extensive experimental results demonstate the effectiveness of our method.