Early classification of time series is becoming increasingly a valuable task for assisting in decision making process in many application domains. In this setting, information can be gained by waiting for more evidences to arrive, thus helping to make better decisions that incur lower misclassification costs, but, meanwhile, the cost associated with delaying the decision generally increases, rendering the decision less attractive. Making early predictions provided that are accurate requires then to solve an optimization problem combining two types of competing costs. This thesis introduces a new general framework for time series early classification problem. Unlike classical approaches that implicitly assume that misclassification errors are cost equally and the cost of delaying the decision is constant over time, we cast the the problem as a costsensitive online decision making problem when delaying the decision is costly. We then propose a new formal criterion, along with two approaches that estimate the optimal decision time for a new incoming yet incomplete time series. In particular, they capture the evolutions of typical complete time series in the training set thanks to a segmentation technique that forms meaningful groups, and leverage these complete information to estimate the costs for all future time steps where data points still missing. These approaches are interesting in two ways: (i) they estimate, online, the earliest time in the future where a minimization of the criterion can be expected. They thus go beyond the classical approaches that myopically decide at each time step whether to make a decision or to postpone the call one more time step, and (ii) they are adaptive, in that the properties of the incoming time series are taken into account to decide when is the optimal time to output a prediction. Results of extensive experiments on synthetic and real data sets show that both approaches successfully meet the behaviors expected from early classification systems.