Siamese networks have been shown to be successful in learning deep representations for multivariate time series verification. However, most related studies optimize a global distance objective and suffer from a low discriminative power due to the loss of temporal information. To address this issue, we propose an end-to-end, neural network-based framework for learning local representations of time series, and demonstrate its effectiveness for online signature verification. This framework optimizes a Siamese network with a local embedding loss, and learns a feature space that preserves the temporal location-wise distances between time series. To achieve invariance to non-linear temporal distortion, we propose building a dynamic time warping block on top of the Siamese network, which will greatly improve the accuracy for local correspondences across intra-personal variability. Validation with respect to online signature verification demonstrates the advantage of our framework over existing techniques that use either handcrafted or learned feature representations.