The goal of early classification of time series is to predict the class value of a sequence early in time, when its full length is not yet available. This problem arises naturally in many contexts where the data is collected over time and the label predictions have to be made as soon as possible. In this work, a method based on probabilistic classifiers is proposed for the problem of early classification of time series. An important feature of this method is that, in its learning stage, it discovers the timestamps in which the prediction accuracy for each class begins to surpass a pre-defined threshold. This threshold is defined as a percentage of the accuracy that would be obtained if the full series were available, and it is defined by the user. The class predictions for new time series will only be made in these timestamps or later. Furthermore, when applying the model to a new time series, a class label will only be provided if the difference between the two largest predicted class probabilities is higher than or equal to a certain threshold, which is calculated in the training step. The proposal is validated on 45 benchmark time series databases and compared with several state-of-the-art methods, and obtains superior results in both earliness and accuracy. In addition, we show the practical applicability of our method for a real-world problem: the detection and identification of bird calls in a biodiversity survey scenario.