Deep Time Series Forecasting with Shape and Temporal Criteria

TL;DR

This paper introduces DILATE and STRIPE++ frameworks that incorporate shape and temporal criteria into deep learning models to improve multi-step time series forecasting, especially for non-stationary signals with sudden changes.

Contribution

It proposes differentiable shape and temporal similarity measures based on relaxed DTW and TDI, enabling new loss functions and kernels for deterministic and probabilistic forecasting.

Findings

Enhanced sharpness of predictions in non-stationary signals

Improved diversity and accuracy in probabilistic forecasts

Validated benefits through extensive experiments on real-world data

Abstract

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic forEcasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.