Time series has numerous application scenarios. However, since many time series data are personal data, releasing them directly could cause privacy infringement. All existing techniques to publish privacy-preserving time series perturb the values while retaining the original temporal order. However, in many value-critical scenarios such as health and financial time series, the values must not be perturbed whereas the temporal order can be perturbed to protect privacy. As such, we propose "local differential privacy in the temporal setting"(TLDP) as the privacy notion for time series data. After quantifying the utility of a temporal perturbation mechanism in terms of the costs of a missing, repeated, empty, or delayed value, we propose three mechanisms for TLDP. Through both analytical and empirical studies, we show the last one, Threshold mechanism, is the most effective under most privacy budget settings, whereas the other two baseline mechanisms fill a niche by supporting very small or large privacy budgets.