Deep time series metric learning is challenging due to the difficult trade-off between temporal invariance to nonlinear distortion and discriminative power in identifying non-matching sequences. This paper proposes a novel neural network-based approach for robust yet discriminative time series classification and verification. This approach adapts a parameterized attention model to time warping for greater and more adaptive temporal invariance. It is robust against not only local but also large global distortions, so that even matching pairs that do not satisfy the monotonicity, continuity, and boundary conditions can still be successfully identified. Learning of this model is further guided by dynamic time warping to impose temporal constraints for stabilized training and higher discriminative power. It can learn to augment the inter-class variation through warping, so that similar but different classes can be effectively distinguished. We experimentally demonstrate the superiority of the proposed approach over previous non-parametric and deep models by combining it with a deep online signature verification framework, after confirming its promising behavior in single-letter handwriting classification on the Unipen dataset.