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Time-series forecasting has caught increasing attention in the AI researchfield due to its importance in solving real-world problems across differentdomains, such as energy, weather, traffic, and economy. As shown in varioustypes of data, it has been a must-see issue to deal with drastic changes,temporal patterns, and shapes in sequential data that previous models are weakin prediction. This is because most cases in time-series forecasting aim tominimize $L_p$ norm distances as loss functions, such as mean absolute error(MAE) or mean square error (MSE). These loss functions are vulnerable to notonly considering temporal dynamics modeling but also capturing the shape ofsignals. In addition, these functions often make models misbehave and returnuncorrelated results to the original time-series. To become an effective lossfunction, it has to be invariant to the set of distortions between twotime-series data instead of just comparing exact values. In this paper, wepropose a novel loss function, called TILDE-Q (Transformation Invariant Lossfunction with Distance EQuilibrium), that not only considers the distortions inamplitude and phase but also allows models to capture the shape of time-seriessequences. In addition, TILDE-Q supports modeling periodic and non-periodictemporal dynamics at the same time. We evaluate the effectiveness of TILDE-Q byconducting extensive experiments with respect to periodic and non-periodicconditions of data, from naive models to state-of-the-art models. Theexperiment results indicate that the models trained with TILDE-Q outperformthose trained with other training metrics (e.g., MSE, dynamic time warping(DTW), temporal distortion index (TDI), and longest common subsequence (LCSS)).

TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting