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This paper addresses the problem of time series forecasting fornon-stationary signals and multiple future steps prediction. To handle thischallenging task, we introduce DILATE (DIstortion Loss including shApe andTimE), a new objective function for training deep neural networks. DILATE aimsat accurately predicting sudden changes, and explicitly incorporates two termssupporting precise shape and temporal change detection. We introduce adifferentiable loss function suitable for training deep neural nets, andprovide a custom back-prop implementation for speeding up optimization. We alsointroduce a variant of DILATE, which provides a smooth generalization oftemporally-constrained Dynamic Time Warping (DTW). Experiments carried out onvarious non-stationary datasets reveal the very good behaviour of DILATEcompared to models trained with the standard Mean Squared Error (MSE) lossfunction, and also to DTW and variants. DILATE is also agnostic to the choiceof the model, and we highlight its benefit for training fully connectednetworks as well as specialized recurrent architectures, showing its capacityto improve over state-of-the-art trajectory forecasting approaches.

Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models