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We present Spectral Differential Privacy (SpDP), a novel form of differential privacy designed to protect the frequency content of time series data that come from wide sense stationary stochastic processes. This notion is motivated by privacy needs in applications with time series data over unbounded time, such as smart meters. First, a notion of differential privacy on the space of (discretized) spectral densities is introduced. A Gaussian-like mechanism for SpDP is then presented that provides differential privacy to the spectral density. Next, a novel streaming implementation is developed to enable real-time use of the proposed mechanism. The privacy guarantee provided by SpDP is independent of the time duration over which data is collected or shared. In contrast, time-domain trajectory-level differential privacy (TrDP) will require noise with large variance to provide privacy over an extended time duration. The technique is numerically evaluated using smart meter data from a single home to compare the utility of SpDP to that of time-domain trajectory-level differential privacy. The noise added by SpDP is substantially smaller than that added by time-domain TrDP, particularly when privacy over long time horizons is sought by TrDP. |
