We propose a neural network-based framework for learning local representations of multivariate time series, and demonstrate its effectiveness for online signature verification. In contrast to related works that optimize a global distance objective, we incorporate a Siamese network into dynamic time warping (DTW), leading to a novel prewarping Siamese network (PSN) optimized with a local embedding loss. PSN learns a feature space that preserves the temporal location-wise distances of local structures. Local embedding, along with the alignment conditions of DTW, imposes a temporal consistency constraint on the sequence-level distance measure while achieving invariance as regards non-linear distortions. Validation on online signature verification datasets demonstrates the advantage of our framework over existing techniques that use either handcrafted or learned feature representations.