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Time series data can be defined as a chronological sequence of observations on a variable of interest. A streaming time series is a time series that arrives continuously at high speed and has a data distribution that may change over time. Streaming time series data usually comes from electronic devices such as sensors and many of the applications dealing with streaming data in Industry 4.0 require real-time responses. Performing real-time forecasting offers the possibility to consider new types of patterns in the incoming streaming data, which is not possible when working with batch models. This paper presents a new approach to detect novelties and anomalies in real-time using a nearest-neighbors based forecasting algorithm. The algorithm works with an offline base model that is updated as stream data arrives following an incremental learning approach. It detects unknown patterns called novelties and anomalies. Novelties are included in the model in an online way and anomalies trigger an alarm as they present unexpected behaviors that need to be specifically analyzed. The algorithm has been tested with Spanish electricity demand data. Results show that the prediction errors obtained when the model is updated considering novelties and anomalies are lower than the errors obtained when the model is not updated. Thus, the model adjusts in real-time to the new patterns of data providing accurate errors and real-time predictions. [ABSTRACT FROM AUTHOR]