Differentially Private Time Series Publishing Based on Multiscale Wavelet Energy Features and Noise Covariance Matrix Optimization

To address the distortion of temporal trends and structures caused by differential privacy noise, this paper proposes a differentially private time-series release method based on multiscale energy features and noise covariance optimization, termed Wavelet Energy and Covariance Optimization-Based Differential Privacy (WECO-DP). The proposed method normalizes time series using fixed public bounds and employs public calibration data separate from the protected input to predetermine scale-specific energy weights, fixed coefficient positions, and the number of retained coefficients at each scale, thereby constructing a fixed wavelet query. Under an adjacency relation defined by a change at a single time point, worst-case sensitivity constraints are established by analyzing the responses of the fixed query to changes at different time positions. The scale-specific energy weights are then incorporated into the noise optimization objective to jointly determine the Gaussian noise variances across scales. Subsequently, a single Gaussian perturbation is applied to the retained wavelet coefficients, and the released series is obtained through the inverse discrete wavelet transform. Theoretical analysis demonstrates that WECO-DP satisfies event-level (ε, δ)-differential privacy. Experimental results on three real-world time-series datasets involving water consumption, electricity consumption, and unemployment rates show that WECO-DP generally achieves lower root mean square error and mean absolute error than five baseline methods under different privacy budgets. Ablation experiments and structure-preservation analysis further demonstrate the contributions of fixed coefficient selection, scale-specific energy weighting, and scale-specific noise variance optimization to release utility. WECO-DP reduces the influence of privacy perturbation on the principal structural information of time series while satisfying event-level privacy constraints, thereby improving the utility of the released data.