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The explosion of data collection has raised serious privacy concerns in users due to the possibility that sharing data may also reveal sensitive information. The main goal of a privacy-preserving mechanism is to prevent a malicious third party from inferring sensitive information while keeping the shared data useful. In this paper, we study this problem in the context of time series data and smart meters (SMs) power consumption measurements in particular. Although Mutual Information (MI) between private and released variables has been used as a common information-theoretic privacy measure, it fails to capture the causal time dependencies present in the power consumption time series data. To overcome this limitation, we introduce the Directed Information (DI) as a more meaningful measure of privacy in the considered setting and propose a novel loss function. The optimization is then performed using an adversarial framework where two Recurrent Neural Networks (RNNs), referred to as the releaser and the adversary, are trained with opposite goals. Our empirical studies on real-world data sets from SMs measurements in the worst-case scenario where an attacker has access to all the training data set used by the releaser, validate the proposed method and show the existing trade-offs between privacy and utility.