Several interpretability methods for convolutional network-based classifiers exist. Most of these methods focus on extracting saliency maps for a given sample, providing a local explanation that highlights the main regions for the classification. However, some of these methods lack detailed explanations in the input space due to upscaling issues or may require random perturbations to extract the explanations. We propose Convolutional Rectifier for Interpretable Time Series Classification, or CRITS, as an interpretable model for time series classification that is designed to intrinsically extract local explanations. The proposed method uses a layer of convolutional kernels, a max-pooling layer and a fully-connected rectifier network (a network with only rectified linear unit activations). The rectified linear unit activation allows the extraction of the feature weights for the given sample, eliminating the need to calculate gradients, use random perturbations and the upscale of the saliency maps to the initial input space. We evaluate CRITS on a set of datasets, and study its classification performance and its explanation alignment, sensitivity and understandability.