Time series prediction typically consists of a data reconstruction phase where the time series is broken into overlapping windows known as the timespan. The size of the timespan can be seen as a way of determining the extent of past information required for an effective prediction. In certain applications such as the prediction of wind-intensity of storms and cyclones, prediction models need to be dynamic in accommodating different values of the timespan. These applications require robust prediction as soon as the event takes place. We identify a new category of problem called dynamic time series prediction that requires a model to give prediction when presented with varying lengths of the timespan. In this paper, we propose a co-evolutionary multi-task learning method that provides a synergy between multi-task learning and co-evolutionary algorithms to address dynamic time series prediction. The method features effective use of building blocks of knowledge inspired by dynamic programming and multi-task learning. It enables neural networks to retain modularity during training for making a decision in situations even when certain inputs are missing. The effectiveness of the method is demonstrated using one-step-ahead chaotic time series and tropical cyclone wind-intensity prediction.